Einstein like (epsilon)-para Sasakian manifolds

Abstract

Einstein like (epsilon)-para Sasakian manifolds are introduced. For an (epsilon)-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 (epsilon)-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 (epsilon)-almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be (epsilon)-para Sasakian is obtained and it is proved that the (epsilon)-para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.