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

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 $(\varepsilon)$-para Sasakian is obtained and it is proved that the $(\varepsilon)$-para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.

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