Geodesic
A contact metric manifold satisfying a certain curvature condition
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 319-333

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $.
Classification : 53C15, 53C25, 53C35
Keywords: contact metric manifolds; Tanaka connection; Jacobi operator 
@article{ARM_1995__31_4_a9,
     author = {Cho, Jong Taek},
     title = {A contact metric manifold satisfying a certain curvature condition},
     journal = {Archivum mathematicum},
     pages = {319--333},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {1995},
     mrnumber = {1390592},
     zbl = {0849.53030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995__31_4_a9/}
}
TY  - JOUR
AU  - Cho, Jong Taek
TI  - A contact metric manifold satisfying a certain curvature condition
JO  - Archivum mathematicum
PY  - 1995
SP  - 319
EP  - 333
VL  - 31
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_1995__31_4_a9/
LA  - en
ID  - ARM_1995__31_4_a9
ER  - 
%0 Journal Article
%A Cho, Jong Taek
%T A contact metric manifold satisfying a certain curvature condition
%J Archivum mathematicum
%D 1995
%P 319-333
%V 31
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_1995__31_4_a9/
%G en
%F ARM_1995__31_4_a9
Cho, Jong Taek. A contact metric manifold satisfying a certain curvature condition. Archivum mathematicum, Tome 31 (1995) no. 4, pp. 319-333. http://geodesic.mathdoc.fr/item/ARM_1995__31_4_a9/