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

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.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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