Two theorems on (ϵ)‐Sasakian manifolds

Abstract

ABSTRACT. In this paper, We prove that every (e)-sasakian manifold is a hypersurface of an indefinite kaehlerian manifold, and give a necessary and sufficient condition for a Riemannian manifold to be an (e)-sasakian manifold.KEY WORDS AND PHRASES: ()-sasakian manifolds; real hypersurface; indefinite kaehlerian manifolds; (e)-almost contact structure.

Curvature and torsion of a legendre curve in (e;d) Trans-Sasakian manifolds

“…The concept of (ε)−Sasakian manifolds were introduced by A. Bejancu and K. L. Duggal [1] and X. Xufeng and C. Xiaoli [23] proved that these manifolds are real hypersurfaces of indefinite Kahlerian manifolds. After, curvature conditions of these manifolds were obtained in [18] and (ε)−almost paracontact manifolds were defined in [17].…”

Some Results on Invariant Submanifolds in an Indefinite Trans-Sasakian Manifold-II

“…J.A.Oubina [2] introduced the notion of a tran sasakian manifold of type (α, β).Trans sasakian manifold is an important kind of sasakian manifold such that α = 1 and β = 1. In 1998, Xu.Xufeng and Chao Xiadi proved that every -sasakian manifold is a hyper surfaces of an indefinite Khalerian manifold and established a necessary and sufficient condition for an odd dimensional Riemannian manifold to be an -sasakian manifold [3]. In [4]U.C.De and Avijit Sarkar introduced and studied the notion ofKenmotsu manifolds with indefinite metric with an example.…”

On a SEMI-SYMMETRIC METRIC CONNECTION IN AN (Ε)-Kenmotsu MANIFOLD

“…Manifolds with indefinite metrics have been studied by several authors. In 1993, Bejancu and Duggal [3] introduced the concept of (ε)-Sasakian manifolds and Xufeng and Xiaoli [20] established that these manifolds are real hypersurfaces of indefinite Kahlerian manifolds. Recently De and Sarkar [9] introduced (ε)-Kenmotsu manifolds and studied conformally flat, Weyl semisymmetric, φ-recurrent (ε)-Kenmotsu manifolds.…”