On $\varphi$-${\cal T}$-Symmetric ($\varepsilon$)-Para Sasakian Manifolds

Punam Gupta

Abstract

The purpose of the present paper is to study the globally and locally ϕ-T-symmetric (ε)-para Sasakian manifold. The globally ϕ-T-symmetric (ε)-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally ϕ-T -symmetric is given. A 3-dimensional (ε) -para Sasakian manifold is locally ϕ-T-symmetric if and only if the scalar curvature r is constant. A 3-dimensional (ε)-para Sasakian manifold with η-parallel Ricci tensor is locally ϕ-T-symmetric. In the last, an example of 3-dimensional locally ϕ-T-symmetric (ε)-para Sasakian manifold is given.