Hamdy abd ellah

Hamdy abd ellah
  • Ph.D.
  • Professor (Full) at Assiut University

About

28
Publications
2,560
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111
Citations
Current institution
Assiut University
Current position
  • Professor (Full)
Additional affiliations
October 1986 - March 2016
Assiut University
Position
  • Professor (Full)

Publications

Publications (28)
Article
Full-text available
As a continuation to the study in [8, 12, 15, 17], we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space E 3. For such surfaces, local study is given and some examples are constructed using computer aided geometric design (CAGD).
Article
Full-text available
In this paper, a kinematic surface using equiform motion of an astroid curve in Euclidean 3-space E 3 is generated. The main results given in this paper: the surface foliated by equiform motion of astroid curve has a constant Gaussian and mean curvatures if motion of astroids is in parallel planes. Also, the geodesic curves on this surface are obta...
Poster
Full-text available
In this work, we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space E 3. For such surfaces, the local study is given and some examples are constructed using computer-aided geometric design (CAGD).
Article
Full-text available
In this paper, motion of Darboux vector on two different space curves in Euclidean 3-space is investigated. The structure of the motion is based on ruled surfaces generated by Darboux vector w. According to this, developability of the considered ruled surfaces are studied. An extensive comparison between these developable ruled surfaces is performe...
Article
Full-text available
The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E 3 . In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided g...
Article
Full-text available
In the present paper, the differential-geometrical framework for parallel bivariate Pareto distribution surfaces is given. Curvatures of a curve lying on , are interpreted in terms of the parameters of P. Geometrical and statistical interpretations of some results are introduced and plotted.
Article
Full-text available
In this paper, we construct and obtain the necessary condition of Weingarten and linear Weingarten translation surfaces in . Special cases of these types are investigated and plotted.
Article
Full-text available
Geometry and kinematics have been intimately connected in their historical evolution and, although it is currently less fashionable, the further development of such connections is crucial to many computer-aided design and manufacturing. In this paper, the evolution of the translation surfaces and their generating curves in E3 are investigated. Inte...
Article
Full-text available
In this paper, a new representation of a cyclic surface by using circles of curvature of a space curve is presented. The conditions on the space curve such that cyclic surface with zero or non zero constant Gaussian curvature are given. The zero second Gaussian curvature is investigated. Also, minimal cyclic surfaces are studied. A procedure to det...
Article
Full-text available
In this paper, a three dimensional surface using equiform motion of a surface of revolution in Euclidean 3-space E 3 is generated. The main results obtained in this paper are that the surface foliated by equiform motion of sphere has a zero scaler curvature if the motion of sphere are in parallel planes. Also, the surface foliated by equiform motio...
Article
Full-text available
We study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies a nontrivial relation between elements of the set {K,K II ,H,H II }, where (K,H) and (K II ,H II ) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Some examples are constructed and plotted.
Article
New in the present paper is a differential-geometrical framework for analyzing statistical problems related to the Weibull distribution using a one-parameter family of affine connections. The geometry of the statistical manifold is given. A development of the relation between the J-divergence and geodesic distance is obtained. Finally, the curvatur...
Article
Full-text available
The present paper intends to investigate the kinematics of a particular type of linear Weingarten surfaces, namely tubular surfaces, in terms of their intrinsic geometric formulas. The evolution equations for the local frame, the first and the second fundamental quantities for the motion are established. The mean curvature flow is studied. Thus the...
Article
One of the most interesting and profound aspects of classical differential geometry is its interplay with the calculus of variations. In fact, the main differential geometric ideas of the calculus of variation occur over and over again and are continually being invented and rediscovered in a vast array of classical and modern differential geometry....
Article
The differential-geometrical framework for analyzing statistical problems related to Pareto distribution, is given. A classical and intuitive way of description the relationship between the differential geometry and the statistics, is introduced [Publicationes Mathematicae Debrecen, Hungary, vol. 61 (2002) 1–14; RAAG Mem. 4 (1968) 373; Ann. Statist...
Article
A representation of a special type of the variational problem on a surface immersed in a hyperbolic space is given. The perturbations of the mean curvature functional are studied. For this study, the corresponding frames are constructed and the polar surfaces of a given surface is established. The technique adapted here is based on Cartan’s methods...
Article
Information geometry (Geometry and Nature) has emerged from the study of invariant properties of the manifold of probability distributions. It is regarded as a mathematical discipline having rapidly developing areas of applications as well as giving new trends in geometrical and topological methods. Information geometry has many applications belong...
Article
We give a representation of the variational problem on a time (space) like surface immersed in a hyperbolic space. The geometric properties of the deformed surfaces are given. The variational problem for the Klein images of 2-parametric continuous motion of a line (kinematic surface) are introduced. The theory of Klein images is applied to a time l...
Article
A brief account of information geometry and the deep relationship between the differential geometry and the statistics is given [N.H. Abdel-All, International Conference on Differential Geometry and its Applications, Cairo University, 19–26 June, Egypt, 2001; Springer Lecture Notes in Statistics, vol. 28, 1985; Math. Syst. Theory 20 (1987) 53]. The...
Article
Full-text available
As it is well known that the most useful method of studying the properties of a curve in a Euclidean space from the standpoint of differential geometry is to make use of the Frenet formulas, in which the curvatures are the essential quantities for the curve. So, the motivation of the present work is to develop the variational problem in our work [C...
Article
Some geometers have been interested in differential geometry of the variational problems connected with general surfaces. During the last few decades, this interest increased rapidly as more researchers became involved and gained results. Specifically one may cite, in this regard, the works of B.Y. Chen [J. London Math. Soc. 6 (2) (1973) 321; Total...
Article
As is well known, the most useful method of studying the properties of a curve in a Euclidean space, from the standpoint of differential geometry, is making use of the Frenet formulas, in which the curvatures are the essential quantities for the curve. So, the motivation of the present work is to develop the variational problem in our work1 by usin...
Article
A surface M isometrically immersed in a Euclidean m-space Em is said to be of null 2-type if its immersion is obtained by harmonic functions and eigenfunctions of the Laplacian ∆ associated with a nonzero eigenvalue. Chen proved that surfaces in E 3 are of null 2-type if and only if they are open portions of circular cylinders.
Article
This work is devoted to the investigation of an m-submanifold, in the Euclidean n-space E n , foliated by a Euclidean (m-1)-plane. We extend results of N. Kuruoğlu and S. Keleş [Karadeniz Univ. Math. J. 6, 41–54 (1983; Zbl 0537.53006)] and of C. Thas [Yokohama Math. J. 26, 157–167 (1978; Zbl 0423.53045)]. The scalar normal curvature is obtained in...
Article
Full-text available
In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set {K, KII, H, HII}, where (K,H) and (KII,HII) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

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