The Chinea–Gonzalez class C5⊕ C12 consists of the almost contact metric manifolds that are locally described as double-twisted product manifolds $I imes_{lambda_1,lambda_2)}M$, I being an open interval, M a Kähler manifold and λ1, λ2 smooth positive functions. In this article, we investigate the behavior of the curvature of C5⊕ C12-manifolds. Particular attention to the N(k)-nullity condition is given and some local classification theorems in dimension 2 n+ 1 ≥ 5 are stated. This allows us to classify C5⊕ C12-manifolds that are generalized Sasakian space forms. In addition, we provide explicit examples of these spaces.

Curvature of $C_5oplus C_{12}$-manifolds

S. De Candia;M. Falcitelli
2019

Abstract

The Chinea–Gonzalez class C5⊕ C12 consists of the almost contact metric manifolds that are locally described as double-twisted product manifolds $I imes_{lambda_1,lambda_2)}M$, I being an open interval, M a Kähler manifold and λ1, λ2 smooth positive functions. In this article, we investigate the behavior of the curvature of C5⊕ C12-manifolds. Particular attention to the N(k)-nullity condition is given and some local classification theorems in dimension 2 n+ 1 ≥ 5 are stated. This allows us to classify C5⊕ C12-manifolds that are generalized Sasakian space forms. In addition, we provide explicit examples of these spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/232266
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