Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold

Sasakian Metric as a Ricci Soliton and Related Results

We prove the following results: (i) A Sasakian metric as a nontrivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group H as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an ηEinstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvatur...

On Generalized Recurrent and Ricci Recurrent Lorentzian Trans-Sasakian Manifolds

The purpose of the paper is to introduce the notion of generalized recurrent Lorentzian transSasakian manifold and study some of the properties of generalized recurrent and Ricci recurrent Lorentzian Trans-Sasakian manifolds.

Cr-submanifolds of a Nearly Trans-sasakian Manifold

Half Lightlike Submanifolds of an Indefinite Trans-sasakian Manifold

We study half lightlike submanifold M of an indefinite transSasakian manifold such that its structure vector field is tangent to M . First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...