Rigidity results for submanifolds in generalized Sasakian space forms (original) (raw)

On pseudo-slant submanifolds of a Sasakian space form

Filomat

In this paper, we study the geometry of the pseudo-slant submanifolds of a Sasakian space form. Necessary and sufficient conditions are given for a submanifold to be pseudo-slant submanifolds, pseudo-slant product, mixed geodesic and totally geodesic in Sasakian manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifolds of Sasakian manifolds and Sasakian space forms.

Some results for anti-invariant submanifold in generalized Sasakian space form

2011

ABSTRACT In this paper we prove some inequalities, relating the scalar curvature R and the mean curvature vector field H of an anti-invariant submanifold in a generalized Sasakian space form M ¯(f 1 ,f 2 ,f 3 ). Also, we obtain a necessary condition for such anti-invariant submanifolds to admit a minimal manifold.

On submanifolds of Sasakian manifolds

Lobachevskii Journal of Mathematics, 2011

The object of the present paper is to introduce a new type of invariant submanifolds, namely, mixed-invariant submanifolds of Sasakian manifolds and to show that everymixed-invariant submanifold of a Sasakian manifold is totally geodesic. 2-quasi-umbilical hypersurface of a Sasakian space form is also studied.

New examples of generalized Sasakian space-forms

Preprint

In this paper we study when a non-anti-invariant slant submanifold of a generalized Sasakian-space-form inherits such a structure, on the assumption that it is totally geodesic, totally umbilical, totally contact geodesic or totally contact umbilical. We obtain some general results (including some obstructions) and we also offer some explicit examples.

On The T Curvature Tensor of Generalized Sasakian Space Form

2015

The objects of the present paper is to characterize generalized Sasakian-space-form satisfying certain curvature conditions on T curavature tensor . In this paper we study T semisymmetric, T flat, T flat and T recurrent generalized Sasakian-space-forms. Generalized Sasakian-space-form satisfying T:S = 0 and T:R = 0 have also been studied. Keywords: T curvature tensor, Generalized Sasakian manifold, T semisymmetric, T flat and T -flat .

On the geometry of pseudo-slant submanifolds of a nearly sasakian manifold

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2018

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We verify some properties of the components of the tensor field acting on that kind of submanifold and find out the necessary and sufficient conditions for them to be parallel. Also, necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, contact pseudo-slant product, D θ , D ⊥ and mixed-geodesic in Sasakian manifold.

On Generalized Sasakian-Space-Forms

ISRN Geometry, 2012

The purpose of the present paper is to characterize pseudoprojectively flat and pseudoprojective semisymmetric generalized Sasakian-space-forms.

On invariant submanifolds of trans-Sasakian manifolds

Proceedings of the Estonian Academy of Sciences, 2012

The object of the present paper is to find necessary and sufficient conditions for invariant submanifolds of trans-Sasakian manifolds to be totally geodesic. As a remark, particular cases of submanifolds of α-Sasakian and β-Kenmotsu manifolds are considered and the difference between the conditions for submanifolds of α-Sasakian and β-Kenmotsu manifolds to be totally geodesic is shown.