Geodesic
A contact metric manifold satisfying a certain curvature condition
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 319-333 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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 
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     author = {Cho, Jong Taek},
     title = {A contact metric manifold satisfying a certain curvature condition},
     journal = {Archivum mathematicum},
     pages = {319--333},
     year = {1995},
     volume = {31},
     number = {4},
     mrnumber = {1390592},
     zbl = {0849.53030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a9/}
}
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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/

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