Shanmukha B.

• M.Sc Ph.D
• Researcher at GM Institute of Technology, Davangere

The object of the present paper is to study Kenmotsu space forms satisfying pseudosymmetric, Ricci-pseudosymmetric and locally-ϕ-symmetric. Further we study the quasi-conformal flat and quasi-conformal semisymmetric Kenmotsu space forms.

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In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized ( k , μ ) {(k,\mu)} -space forms and show that the generalized ( k , μ ) {(k,\mu)} space form is either isometric to a sphere or a certain warped product under some geometric conditions.

In this paper, we study M -projective curvature tensors on an ( LCS ) 2 ⁢ n + 1 {(\mathrm{LCS})_{2n+1}} -manifold. Here we study M -projectively Ricci symmetric and M -projectively flat admitting spacetime.

In the present frame work, we study the properties of \(\eta\)-Ricci soliton on Kenmotsu manifold and also analysed the generalized gradient Ricci soliton equation satisfying some conditions.

In the present frame work, we studied the semi generalized recurrent, semi generalized ϕ -recurrent, extended generalized ϕ -recurrent and concircularly locally ϕ -symmetric on generalized Sasakian space forms.

The object of the present paper is to study some geometric conditions for an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. Further we consider concircular curvature tensor satisfying some geometric conditions of an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. In extension, we build an example o...

In this paper, we study the projective curvature tensor on generalized (k, µ)-space forms. Here we study the projectively flat, ξ-projectively flat, pseudopro-jectvely flat, h-projectively semisymmetric, ϕ-projectively semisymmetric, and P · S on generalized (k, µ)-space forms.

The aim of the present paper is to study pseudo-symmetric, Ricci generalized pseudo-symmetric and generalized Ricci recurrent N(k)-Paracontact Metric Manifolds.

In this paper we have studied Ricci symmetric and Ricci pseudosymmetric generalized (k,µ)-space forms and generalized (k,µ)-space forms with quasi umblical hypersurface and τ-flat curvature tensor

In this paper, we study W2-pseudosymmetric, W2-locally symmetric, W2-locally φ-symmetric and W2-φ-recurrent generalized Sasakian space form. Further, illustrative examples are given.

In this paper, we studied generalized Sasakian space forms admitting Sasakian structure with respect to the quarter symmetric metric connection and the locally ϕ-symmetric, η-recurrent, ϕ-recurrent and flatness of projective curvature tensor on generalized Sasakian space forms. We establish the relation between the Riemannian connection and the qua...

The purpose the present paper is to study M-projective pseudosymmetric, φ-M-projectivelly flat and M-projectivelly flat Lorentzian ᾳ-Sasakian manifold. Here we also prove that a Lorentzian ᾳ-Sasakian manifolds satisfying 𝑀(𝑋,𝑌)⋅𝑅(𝑈,𝑉)𝑍=0 is an Einstein manifold. Moreover we presented an example of Lorentzian ᾳ-Sasakian manifold.

The purpose the present paper is to study M-projective pseudosymmetric, 𝜙-𝑀-projectivelly flat and M-projectivelly flat Lorentzian 𝛼-Sasakian manifold. Here we also prove that a Lorentzian 𝛼-Sasakian manifolds satisfying 𝑀(𝑋,𝑌)⋅𝑅(𝑈,𝑉)𝑍=0 is an Einstein manifold. Moreover we presented an example of Lorentzian 𝛼-Sasakian manifold.

C-Bochner pseudosymmetric LP-Sasakian manifold and LP-Sasakian manifold satisfying B(ξ, X) · B = 0, B(ξ, U) · R = 0 and B(ξ, X) · S = 0 have been studied. Finally an example of LP Sasakian manifold has been constructed.

The object of the present paper is to study the Lorentzian α-Sasakian Manifold satisfying M(X, Y)·W 2 = 0, W_2-Pseudosymmetric, φ−W_2-flat.

The object of the present paper is to study a Para-Sasakian manifold admitting a quarter symmetric metric connection satisfying Z ̅∘S ̅=0, R ̅∘Z ̅=0, Z ̅∘R ̅=0 and ξ-concircularly flatness.