Generalized Sasakian-space-forms

Abstract

Abstract. We study contact metric and trans-Sasakian generalized Sasakian-space-forms. We also give some interesting examples of generalized Sasakian-space-forms by using warped products and conformal changes of metric.

Generalized S-space-forms with two structure vector fields

“…Brought to you by | Biblioteca de la Universidad de Sevilla Authenticated Download Date | 10/5/16 7:50 AM Now, by using (1.2) and the results of O'Neill [12] concerning the Riemannian connections and curvature tensor fields of warped products (see Lemmas 4.6 and 4.7 of [1]), a straightforward calculation proves that M is a generalized S-space-form with functions:…”

“…Thus, an almost-Hermitian manifold (M, J, g) is said to be a generalized More in general, K. Yano [14] introduced the notion of f -structure on a (2m + s)-dimensional manifold as a tensor field f of type (1,1) and rank 2m satisfying f 3 + f = 0. Almost complex (s = 0) and almost contact (s = 1) structures are well-known examples of f -structures.…”

“…) be a generalized Sasakian-space-form [1] with functions f 1 , f 2 and f 3 and let M be an isometrically immersed (orientable) hypersurface of M such that the vector field ξ is always tangent to M . If N denotes the unit normal vector field of M in M and we put…”

“…Consequently, new examples of generalized S-space-forms can be obtained from the examples of generalized Sasakian-space-forms given in [1]. In particular, if N (c) is a complex-space-form of constant holomorphic curvature c, then M = R× h2 (R× h1 N (c)) is a generalized S-space-form (h 1 , h 2 > 0 differentiable functions on R) with functions:…”

“…Furthermore, the hypothesis of (ii) holds, for example, for metric f -K-contact manifolds too. On the other hand, the above theorem can be considered as the version for generalized Sspace-forms of Theorem 12.7 of [13] for generalized complex-space-forms and of either the main theorem in [5] or Theorem 3.4 in [1] for generalized Sasakian-space-forms. Now, we are interested in generalized S-space-forms with a general function F 2 .…”