Indefinite Almost Paracontact Metric Manifolds
We introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/846195 |
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| Summary: | We introduce the concept of (ε)-almost paracontact manifolds,
and in particular, of (ε)-para-Sasakian manifolds. Several examples are presented. Some
typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are
obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent
or proper Ricci-recurrent, then it cannot admit an (ε)-para Sasakian structure. We
show that, for an (ε)-para Sasakian manifold, the conditions of being symmetric, semi-symmetric,
or of constant sectional curvature are all identical. It is shown that a symmetric
spacelike (resp., timelike) (ε)-para Sasakian manifold Mn is locally isometric to a pseudohyperbolic
space Hνn(1) (resp., pseudosphere Sνn(1)). At last, it is proved that for an (ε)-para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric,
and Einstein are all identical. |
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| ISSN: | 0161-1712 1687-0425 |