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) $-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.0378
- arXiv:
- arXiv:1203.0378
- Bibcode:
- 2012arXiv1203.0378K
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematical Physics;
- 53C25;
- 53C50