Generalized Sasakian-space-forms. (English) Zbl 1064.53026

Alegre, Pablo; Blair, David E.; Carriazo, Alfonso

Isr. J. Math. 141, 157-183 (2004).

The authors introduce generalized Sasakian-space-forms and study their basic properties. They state that every generalized Sasakian-space-form with a \(K\)-contact structure is a Sasakian manifold, and, if the dimension is \(\geq5\), a Sasakian-space-form. The conditions for a generalized Sasakian-space-form to be a contact metric manifold are investigated. To construct many examples of these manifolds the authors use a wide variety of geometric constructions, such as Riemannian submersions, product manifolds, warped products, conformal transformations, \(D\)-homothetic deformations and \(D\)-conformal deformations. Some further results on generalized complex-space-forms are also stated.

Reviewer: Neda Bokan (Beograd)

MSC:

53C25

Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

Riemannian submersion; Sasakian-space-forms; \(K\)-contact structure

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