In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.

A Sasakian structure S=(;;;;g) on a manifold M is called positive if its basic rst Chern class c 1 (F) can be represented by a positive (1;1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a comple...

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.

A transformation of an n-dimensional Riemannian manifold M , which transforms every geodesic circle of M into a geodesic circle, is called a concircular transformation. A concircular transformation is always a conformal transformation. Here geodesic circle means a curve in M whose first curvature is constant and second curvature is identically zero. Thus, the geometry of concircular transformat...

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...

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form˜M(c) of constant ϕ-sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold. 1. Introduction. Let˜M be an m-dimensional almost contact manifold endowed with an almost contact structure (ϕ,ξ,...