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Ricci tensors on trans-Sasakian 3-manifolds

Wang Wenjie
Liu Ximin

In this paper, it is proved that a trans-Sasakian 3-manifold is locally symmetric if and only if it is locally isometric to the sphere space S3(c2), the hyperbolic space H3(-c2), the Euclidean space R3, the product space R x S2(c2) or R x H2(-c2), where c is a nonzero constant. Some examples are constructed to illustrate main results. We also give some new conditions for a compact trans-Sasakian 3-manifold to be proper.

Keywords: Trans-Sasakian 3-manifold, Ricci tensor, local symmetry, space form