Einstein like $(\varepsilon)$-para Sasakian manifolds

Abstract

Einstein like $(\varepsilon)$-para Sasakian manifolds are introduced. For an $(\varepsilon)$-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 $(\varepsilon)$-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 $(\varepsilon)$-almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be $(\varepsilon)$