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arXiv · 1203.0378

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

Sadik Keleş·Erol Kiliç·Mukut Mani Tripathi·Selcen Yüksel Perktaş
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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) $-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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Sadik Keleş, Erol Kiliç, Mukut Mani Tripathi, Selcen Yüksel Perktaş. 2012-03-02. Einstein like $(\varepsilon)$-para Sasakian manifolds. https://arxiv.org/abs/1203.0378

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