A Study of Conformal $$\eta$$-Einstein Solitons on Trans-Sasakian 3-Manifold

On Eta-einstein Sasakian Geometry

A compact quasi-regular Sasakian manifold M is foliated by onedimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold Z. In the case when the transverse space Z is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian ...

On an Einstein Projective Sasakian Manifold

In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere S(1). It has also been proved that if in an Einsten-Sasakian manifold the relation K(X, Y ).P = 0 holds, then it is locally isometric with a unit sphere S(1). AMS Mathematics Subject Classif...

Cr-submanifolds of a Nearly Trans-sasakian Manifold

On Sasakian-Einstein Geometry

In 1960 Sasaki [Sas] introduced a type of metric-contact structure which can be thought of as the odd-dimensional version of Kähler geometry. This geometry became known as Sasakian geometry, and although it has been studied fairly extensively ever since it has never gained quite the reputation of its older sister – Kählerian geometry. Nevertheless, it has appeared in an increasing number of dif...

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.