Einstein like -para Sasakian manifolds

Abstract

Einstein like -para Sasakian manifolds are introduced. For an -para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like -para Sasakian manifold is obtained and it is shown that the scalar curvature in this case must satisfy certain differential equation. A necessary and sufficient condition for an -almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be -para Sasakian is obtained and it is proved that the -para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.

Keywords

• Einstein like -para Sasakian manifold
• indefinite locally Riemannian product manifold.