A contact metric manifold satisfying a certain curvature condition

Cho, Jong Taek

Archivum mathematicum, Tome 31 (1995) no. 4, pp. 319-333.

Résumé

In the present paper we investigate a contact metric manifold satisfying (C) $(\bar{\nabla }_{\dot{\gamma }}R)(\cdot ,\dot{\gamma })\dot{\gamma }=0$ for any $\bar{\nabla }$-geodesic $\gamma $, where $\bar{\nabla }$ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma $. Also, we prove a structure theorem for a contact metric manifold with $\xi $ belonging to the $k$-nullity distribution and satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma $.

Détail

Classification : 53C15, 53C25, 53C35
Keywords: contact metric manifolds; Tanaka connection; Jacobi operator