| Title:
|
A contact metric manifold satisfying a certain curvature condition (English) |
| Author:
|
Cho, Jong Taek |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
319-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $. (English) |
| Keyword:
|
contact metric manifolds |
| Keyword:
|
Tanaka connection |
| Keyword:
|
Jacobi operator |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| MSC:
|
53C35 |
| idZBL:
|
Zbl 0849.53030 |
| idMR:
|
MR1390592 |
| . |
| Date available:
|
2008-06-06T21:29:47Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107554 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
