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Einstein like para Sasakian manifolds

Auther : SADIK KELES, EROL KILIC, MUKUT MANI TRIPATHI AND SELCEN YÛKSEL PERKTAS

-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.
Keywords: Einstein like <$>(\varepsilon )<$>-para Sasakian manifold; indefinite locally Riemannian product manifold.

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