let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.

We find Ricci curvature bounds for pointwise semi-slant warped products submanifolds in non-Sasakian generalized Sasakian space forms this work, and analyze the equality case of inequality. The derived inequality is also used to develop a number applications.

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen’s basic inequality between the main intrinsic invariants of the submanifold namely, its pseudosectional curvature and pseudosectional curvature on one side and the main extrinsic invariant namely, squared pseudomean curvature on the other side with respect to the TanakaWebster connection. Moreove...

We begin this review with a brief history of the subject for our exposition shall have little to do with the chronology. In 1960 Sasaki [Sas 1] introduced a geometric structure related to an almost contact structure. This geometry became known as Sasakian geometry and has been studied extensively ever since. In 1970 Kuo [Kuo] refined this notion and introduced manifolds with Sasakian 3-structur...

In this article, we derive Chen’s inequalities involving ?-invariant ?M, Riemannian invariant ?(m1,?,mk), Ricci curvature, ?k(2?k?m), the scalar curvature and squared of mean for submanifolds generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application obtain inequality, first derived Chen inequality bi-slant submanifold Sasakian-space-forms.

We obtain some classification results and the stability conditions of nonminimal biharmonic anti-invariant submanifolds in Sasakian space forms. MSC 2000: 53C42 (primary); 53B25 (secondary)

Sasakian manifolds provide rich source of constructing new Einstein manifolds in odd dimensions [2]. They play some important role in the superstring theory in mathematical physics [19, 20]. There is a renewed interest on Sasakian manifolds recently. The present paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics H (definition in (1.2)) and some o...