In this paper we study C-Bochner pseudosymmetric generalized Sasakian-space-forms and such space-forms with C-Bochner curvature tensor \(B\) satisfying the conditions \(B(\xi , X)\cdot S=0\), \(B(\xi , X)\cdot R=0\) and \(B(\xi , X)\cdot B = 0\), where \(R\) and \(S\) denotes the Riemann curvature tensor and Ricci tensor of the space-form, respectively.

On the C-Bochner Curvature Tensor of Generalized Sasakian-Space-Forms

We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.

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Slant lightlike submanifolds of an indefinite sasakian manifold

In this paper, we study the geometry of indefinite generalized Sasakian space form ¯ M(f1,f2,f3) admitting a generic lightlike subman- ifold M subject such that the structure vector field of ¯ M(f1,f2,f3) is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

/pdf/indefinite-generalized-sasakian-space-form-admitting-a-3kruge065a.pdf

Indefinite generalized sasakian space form admitting a generic lightlike submanifold

We study totally contact umbilical slant lightlike submanifolds of indefinite cosymplectic manifolds. We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds in indefinite cosymplectic manifolds other than totally contact geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite cosymplectic space forms. Finally we give characterization theorems on minimal slant lightlike submanifolds.

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Nonexistence of Totally Contact Umbilical Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

We introduce golden GCR-lightlike submanifolds of golden semi-Riemannian manifolds. We investigate several properties of such submanifolds. Moreover, we find some necessary and sufficient conditions for minimal golden GCR-lightlike submanifolds of golden semi-Riemannian manifolds.

Golden GCR-Lightlike Submanifolds of Golden Semi-Riemannian Manifolds

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of \({R^{9}_{2}}\) and prove some characterization Theorems.

Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

We study the semiparallel lightlike hypersurface of an indefinite cosymplectic space forms which are tangent to the structure vector field.

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Semi-parallel lightlike hypersurfaces of indefinite cosymplectic space forms

Abstract The paper is mainly devoted to the study of the geometry of screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold. The main result is a characterisation theorem for screen conformal lightlike hypersurfaces of an indefinite cosymplectic space form. The examples of totally geodesic, screen homothetic and screen conformal lightlike hypersurfaces are also given.

Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold

In this paper we introduce the notion of lightlike submanifolds of an indefinite cosymplectic manifold. We have studied the invariant, contact CR, contact screen Cauchy-Riemann (contact SCR) lightlike submanifolds of an indefinite cosymplec- tic manifold. We give the condition under which lightlike submanifold of an indefinite cosymplectic manifold is minimal. We have also studied totally contact umbilical lightlike submanifold. Examples of lightlike submanifold of an indefinite cosymplectic manifold have also been given. Mathematics Subject Classication

https://www.degruyter.com/view/j/aicu.2012.lviii.issue-1/v10157-011-0048-6/v10157-011-0048-6.pdf

Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

In this paper, we study semi-symmetric, Ricci semi-symmetric lightlike hypersurfaces of a indeflnite generalized Sasakian space form with structure vector fleld tangent to hypersurface. We obtain the condition for Ricci tensor of lightlike hypersurface of indeflnite generalized Sasakian space form to be symmetric and parallel.

Abhitosh Upadhyay

Papers

Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

Semi-parallel lightlike hypersurfaces of indefinite cosymplectic space forms

Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold

Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

Semi-symmetric and ricci semi-symmetric lightlike hypersurfaces of an indefinite generalized sasakian space form