期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2010
卷号：2010
DOI：10.1155/2010/846195
出版社：Hindawi Publishing Corporation
摘要：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 𝐻𝑛𝜈(1) (resp., pseudosphere 𝑆𝑛𝜈(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.
