# Mahmut ErgütNamık Kemal Üniversitesi · Department of Mathematics

Mahmut Ergüt

Full Professor

## About

108

Publications

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685

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Citations since 2016

## Publications

Publications (108)

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be...

In this paper, we consider the problem of finding the hyper-surface M n in the Euclidean (n+1)-space R^{n+1} that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper half-space R^3_{+}(u) with lowest gravity center, for a fixed unit vector u...

In the present paper, we discuss the singular minimal surfaces in a Euclidean 3−space R 3 which are minimal. In fact, such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the usual condition of singular minimality by using a special semi-symmetric metric connection instead of the Levi-C...

In this paper, we study and classify singular minimal translation surfaces in a Euclidean space of dimension 3 endowed with a certain semi-symmetric (non-)metric connection.

In this paper, we investigate pointwise slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We obtain some characterizations for such a submersion. Also we find curvature relations between the total manifold and the base manifold.

In this paper, we study the problem of finding affine factorable surfaces in a 3−dimensional isotropic space I3 with prescribed Gaussian (K) or mean (H) curvatures. Because the absolute figure of I3, by permutation of coordinates two different types of these surfaces
appear. We firstly classify the affine factorable surfaces of type 1 with K,H cons...

In this paper, we consider the problem of finding the hypersurface M^n in the Euclidean (n+1)-space R^{n+1} that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the hypersurfaces in the upper halfspace (R^{n+1})_{+} with lowest gravity center, for a fixed unit ve...

In this paper we study the polynomial affine translation surfaces in E3
with constant curvature. We derive some non-existence results for such
surfaces. Several examples are also given by figures.

In this paper, we investigate the Hasimoto surfaces in Euclidean 3-space. Firstly, we investigate the geometric properties of these surfaces in Euclidean 3-space. Especially, we obtain the curvatures of Hasimoto surface according to Bishop frame. Then we give some characterization of parameter curves obtained according to Bishop frame of Hasimoto s...

In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbs...

In this paper, we characterize and classify helix surfaces with principal direction relatived to a space-like and light-like, constant direction in the Minkowski 3-space.

In this paper, we introduce canonical principal direction (CPD) submanifolds with higher codimension in Euclidean spaces. We obtain the complete classification of surfaces endowed with CPD in the Euclidean 4-space.

In this paper, we obtain the mean curvature of a A-net surface in three dimensional Heisenberg group H3. Moreover, we give some characterizations of this surface according to Levi- Civita connections of H3. Using the mean curvature, a new characterization for the cmc A- net surface. Finally, we draw cmc A- net surface by Mathematica.

In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.

In this paper, we describe (linear) Weingarten affine translation surfaces of first kind in the isotropic 3-space. In addition, we obtain such surfaces that satisfy certain equations in terms of the position vector and the Laplace operator.

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their associated graph surfaces in th...

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Minkowski space. First, we get so...

In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples.

In this paper, we completely classify the homothetical hypersurfaces having
null Gauss-Kronocker curvature in a Euclidean (n+1)-space. Several applications
to the production functions in economics are also given.

In this paper, we introduce the factorable surfaces in the pseudo-Galilean space G(3)(1) and completely classify such surfaces with null Gaussian and mean curvature. Also, in a special case, we investigate the factorable surfaces which fulfill the condition that the ratio of the Gaussian curvature and the mean curvature is constant in G(3)(1).

The present authors, in [3], classified the composite functions of the form f = F (h1 (x1) x ::: x hn (xn)) via the Allen determinants used to calculate the Allen's elasticity of substitution of production functions in microeconomics. In this paper, we adapt this classification to the homothetical hypersurfaces in the Euclidean spaces. An applicati...

We study the surfaces corresponding to solutions of the localized induction equation in the pseudo-Galilean space G_{1}^3. We classify such surfaces with null curvature and characterize some special curves on these surfaces in G_{1}^3.

The present authors, in [3], classiﬁed the composite functions of the form $f=F\left( h_{1}\left( x_{1}\right) \times
...\times h_{n}\left( x_{n}\right) \right) $ via the Allen determinants used to calculate the Allen’s elasticity of substitution of production functions in microeconomics. In this paper, we adapt this classiﬁcation to the homothetic...

In this paper, we derive an explicit formula for the Allen determinants of com-posite functions of the form: f (x) = F (h 1 (x 1) × · · · × h n (x n)) . We completely classify the composite functions by using their Allen determinants. Some applications of Allen determinants to production models are also given.

In this paper, we completely classify the homothetic functions of 2 variables by using their Allen’s matrices. We give some applications of Allen’s matrices to composite functions. Several geometric results are also obtained for graphs of homothetic functions.

In this paper, we study non-null curves of Tzitzeica type in Minkowski 3-space . We find a simple link between Tzitzeica curves and Rectifying curves in. Next, we derive certain results for non-null general helices and pseudospherical curves to satisfy Tzitzeica condition. Further, we interest Tzitzeica pseudospherical indicatrices of a spacelike c...

In this paper, we study non-null curves of Tzitzeica type in Minkowski 3-space 3 1 E . We find a simple link between Tzitzeica curves and Rectifying curves in 3 1 E . Next, we derive certain results for non-null general helices and pseudospherical curves to satisfy Tzitzeica condition in 3 1 E . Further, we interest Tzitzeica pseudospherical indica...

B.-Y. Chen [7] derived an explicit formula for the Hessian determinants of composite functions defined by f = F (h1 (x1) +. + hn (xn)). In this paper, we introduce a new formula for the Hessian determinants of composite functions of the form f = F (h1 (x1) +. + hn (xn)). Several applications of the new formula to the well-known Cobb-Douglas product...

: In this paper, we study inextensible flows of spacelike curves on S 2 1 . We obtain partial differential equations in terms of inextensible flows of spacelike curves according to Sabban frame on S 2 1 .

In this paper, we study inextensible flows of b-m1 developable surfaces of biharmonic new type b-slant helix in the Sol3. We characterize one parameter family of the b-m1 developable surfaces in terms of their Bishop curvatures.

: In this paper, ruled surfaces of type II in a three-dimensional Pseudo-Galilean space are given. By studying its Gauss map and Laplacian operator, we obtain a classification of ruled surfaces of type II in a three-dimensional Pseudo-Galilean space.

In this paper, ruled surfaces of type II in a three-dimensional Pseudo-Galilean space are given. By studying its Gauss map and Laplacian operator, we obtain a classification of ruled surfaces of type II in a three-dimensional Pseudo-Galilean space.

In this paper, we study inverse surfaces in Minkowski space E 3 1 . We obtain various relations between these surfaces. Also we give some necessary and sufficient conditions so that the the inverse surface of tangent developable of a timelike curve is flat or minimal in E 3 1 .

In this paper, we establish equiform diﬀerential geometry of curves in 4- dimensional Galilean space G4. We obtain the angle between the equiform Frenet vectors and their derivatives in G4. Also, we characterize generalized helices with respect to their equiform curvatures.

In this paper, we study involute curve of biharmonic curve in the special three-dimensional f-Ricci symmetric para-Sasakian manifold P. We characterize involute curve of biharmonic curve in terms of curvature and torsion of biharmonic curve in the special three-dimensional f-Ricci symmetric para-Sasakian manifold P. Finally, we find out explicit pa...

In this paper, Theorem 3.2 and Proposition 3.2 in the paper which is cited in the title are corrected.

In this paper, we define the inverse surface of a tangent developable surface
with respect to the sphere S_{c}(r) with the center $c\in \mathbb{E}^{3}$ and
the radius r in 3-dimensional Euclidean space $\mathbb{E}^{3}$. We obtain the
curvatures, the Christoffel symbols and the shape operator of this inverse
surface by the help of these of the tange...

In this paper, we study the inverse surfaces in 3-dimensional Euclidean space
$\mathbb{E}^{3}$. We obtain some results relating Christoffel symbols, the
normal curvatures, the shape operators and the third fundamental forms of the
inverse surfaces

Special curves and their characterizations are one of the main area of
mathematicians and physicians.
As a special curve we will mainly focus on Mannheim curve which has the
following relation: k1={\beta}(k1^2+k2^) where k1 and k2 are curvature and
torsion, respectively.
In the present paper we define Mannheim curves for 4-dimensional Galilean
spac...

The aim of this work is to study the Mannheim curves in 3-dimensional
Galilean and Pseudo - Galilean space. We obtain the characterizations between
the curvatures and torsions of the Mannheim partner curves.

We define an extended null scroll in Minkowski 3-space ℝ 1 3 which is obtained by a null line moving with (proper) null frame along a null curve. We prove the theorem due to Bonnet, well known in the 3-dimensional Euclidean space, for an extended null scroll. We calculate the geodesic and normal curvature of a curve on the extended null scroll.

In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E31. We get the necessary and sufficient conditions for the null Mannheim curves. Then we investigate the null and timelike or spacelike generalized helix as the null Mannheim curve and timelike or spacelike Mannhe...

We define a support function for curves with constant cone curvature κ in the 2-dimensional light-like cone and the evolute-involute curves. Then we characterize curves which satisfy eigenvalue equations for the support function in relation to the evolute-involute curves.

In this article, we study matrix representation of biharmonic curves in 3-dimensional Kenmotsu manifold. We characterize Frenet frame of the biharmonic curves in terms of their curvature and torsion in special 3-dimensional Kenmotsu manifold K.

We study the Euler-Savary formula for planar curves in the light-like cone. We first define the associated curve of a curve in the two-dimensional light-like cone Q 2 . Then, we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional light-like cone Q 2 .

In this study, we define non-null k-slant helices in Minkowski 3-space and give some characterizations for the non-null k-slant helix.

We consider curves of AW(k)-type, 1≤3, in Lorentzian space. We give curvature conditions of these kind of curves. Furthermore, we study harmonic curvatures of curves of AW(k)-type. We investigate that under what conditions AW(k)-type curves are helix. Some related theorems and corollaries are also proved. Editorial remark: There are doubts about a...

In this study, firstly, we give curvature conditions of AW(k)-type (1≤k≤3) curves. Then considering AW(k)-type curves, we investigate Bertrand curves γ:I→L3 with κ1(s)≠0 and κ2(s)≠0. We show that there are Bertrand curves of AW(1)-type and AW(3)-type. Moreover, we study weak AW(2)-type and AW(3)-type conical geodesic curves in L3.

We investigate hypersurfaces with constant scalar curvature in a Hessian manifold of constant curvature and obtain two theorems on hypersurfaces of Hessian manifolds with non-negative constant curvature.

For an n-dimensional manifold N immersed in a 4n-dimensional quaternion space form an integral inequality is obtained, involving the mean curvature vector and the norm of the second fundamental form.

We investigate new characteristic properties for two dimensional null scroll in the n-dimensional Lorentzian space ℝ 1 n and we examine the sufficient and necessary conditions for null scroll M to be totally geodesic. We also give Massey’s Theorem for the two dimensional null scroll in ℝ 1 n which is well known for the ruled surfaces in the Euclide...

In this paper, the characterization of an admissible curve which is not null in pseudo-Galilean 3-space is given. Furthermore the differential equation which expresses the given characterization is solved.

We investigate null curves of the AW(k)-type (1 ≤ k ≤ 3) in the 3-dimensional Lorentzian space, L

In this Letter, we investigate curves of AW(k)AW(k)-type (1⩽k⩽3)(1⩽k⩽3) in the 3-dimensional null cone and we give curvature conditions of these kind of curves.

T. Ikawa obtained an ordinary differential equation for the circular helix. Recently, the helix have been investigated by many differential geometers such as T. Ikawa, H. Balgetir, M. Bektas, M. Ergut, N. Ekmekci and H. H. Hacisalihoglu. In this paper, making use of this author's methods, we obtained characterizations of helix for a curve with resp...

Let (M, g) be a compact immersed hypersurface of (Rn+1,<, >), λ1 the first nonzero eigenvalue, α the mean curvature, ρ the support function, A the shape operator, vol(M) the volume of M, and S the scalar curvature of M. In this paper, we established some eigenvalue inequalities and proved the above. 1) 1/n ∫M ||A||2 ρ2 dv ≥ ∫M α2ρ2dv, 2) ∫M α2ρ2dv...

In this paper, the distribution parameter of a null scroll which is obtained by a null straight line moving along a null curve and some theorems related to the distribution parameter are given in the 3-dimensional Minkowski space ℝ³1.

Izumiya and Takeuchi (2003) obtained some characterizations for Ruled surfaces. Turgut and Hacisalihoğlu (1998) defined timelike
Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi (1995) and Jung and Pak (1996) studied
Ruled surfaces. This study uses the method in (Izumiya and Takeuchi, 2003) to investigate cylindri...

In this paper, we study a reliable numerical approximation of the linear and non-linear Klein–Gordon equations by using the Adomian's decomposition method. The solution is calculated in the form of a series with easily computable components. We prove the convergence of this method applied to the non-linear Klein–Gordon equation. The numerical resul...

T. Ikawa obtained in [Tsukuba J. Math. 9, 353–371 (1985; Zbl 0588.53017)] the following characteristic ordinary differential equation ∇ X ∇ X ∇ X X-K∇ X X=0,K=k 2 -τ 2 for the circular helix which corresponds to the case that the curvatures k and τ of a time-like curve c on the Lorentzian manifold M are constant. In this paper, making use of method...

Purpose
Aims to solve singular two‐point boundary value problems, linear and non‐linear by using modified and standard decomposition methods, respectively.
Design/methodology/approach
The approximate solution of this problem is calculated in the form of series with easily computable components.
Findings
The accuracy of the presented numerical met...

In this paper, the decomposition method is implemented for solving the linear and nonlinear diffusion and convection-diffusion equations. The approximate solutions of these problems are calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with analytical, appro...

In this paper, improved Jacobi elliptic function method is used to construct new exact doubly periodic wave solutions of the generalized shallow water wave equation (GSWW). The method can also be applied to other nonlinear partial differential equations (PDEs) or systems in mathematical physics.

A steady flow problem of a viscous incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers. A problem of such type has been solved by applying LAD method given by Roache [Comp. Fluids 3 (1975) 179]. The resulting system of linear equations is solved by Adomian decom...

In this paper, we obtained an integral formula for compact sub-manifold in R m .

The Adomian decomposition method is used to implement the nonhomogeneous multidimensional partial differential equation model problem. The analytic solution of the equation is calculated in the form of a series with easily computable components.The nonhomogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vani...

The purpose of this paper is introduce nondegenerate ruled surfaces in L 3 which are said to be B-scrolls. We defined the central point, the curve of striction, pseudo-orthogonal trajectory in a B-scroll and obtained some theorems related to these structures in the 3-dimensional Lorentzian space L 3 . We gave also the distribution parameter of a B-...

Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized form which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+y m =x where x is a stochastic process and L is a linear stochastic operator. We study an analytic solution...

This paper emphasises the important extensions of eigenvalue inequalities to submanifolds in pseudo Euclidean space. It considers x: Mn →φ Smm →i Esm+1, where φ is an isometric immersion, i is the inclusion, k-type submanifold in pseudo-Euclidean space is given and some eigenvalue inequalities are extended to k-type submanifold of pseudo-Euclidean...

In [Q. J. Math., Oxf. II. Ser. 49, 35–41 (1998; Zbl 0906.53003)] S. Deshmukh proved that a compact and connected immersed hypersurface M of ℝ n+1 which has a positive Ricci curvature and whose scalar curvature r satisfies r=λ 1 (n-1), λ 1 being the first nonzero eigenvalue of Δ on M, isometric to S n (c) for some constant c. In the paper, we discus...

B. Y. Chen [Indiana Univ. Math. J. 20, 1175-1185 (1971; Zbl 0219.53047)] and H. Sun [Tsukuba J. Math. 20, 45-50 (1996; Zbl 0888.53039)] have studied pseudo-umbilical submanifolds. In this paper, we generalize the compact pseudo-umbilical space-like submanifolds with parallel mean curvature in a pseudo-Riemannian space.

In this paper, the characterization of the spherical curves in 3-dimensional Lorentzian space is given which corresponds to the 3-dimensional Euclidean space.