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 $.
@article{107554,
author = {Jong Taek Cho},
title = {A contact metric manifold satisfying a certain curvature condition},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {319-333},
zbl = {0849.53030},
mrnumber = {1390592},
language = {en},
url = {http://dml.mathdoc.fr/item/107554}
}
Cho, Jong Taek. A contact metric manifold satisfying a certain curvature condition. Archivum Mathematicum, Tome 031 (1995) pp. 319-333. http://gdmltest.u-ga.fr/item/107554/
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