| Title:
|
Infinitesimal characterization of almost Hermitian homogeneous spaces (English) |
| Author:
|
Console, Sergio |
| Author:
|
Nicolodi, Lorenzo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
713-721 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer $k_H$, the covariant derivatives of the curvature tensor up to order $k_H+2$ and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given. (English) |
| Keyword:
|
almost Hermitian homogeneous spaces |
| Keyword:
|
Singer invariant |
| MSC:
|
53C30 |
| MSC:
|
53C55 |
| idZBL:
|
Zbl 1020.53031 |
| idMR:
|
MR1756547 |
| . |
| Date available:
|
2009-01-08T18:56:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119125 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[KT] Kowalski O., Tricerri F.: A canonical connection for locally homogeneous Riemannian manifolds.D. Ferus et al. Proc. Conf. Global Diff. Geom. and Global Analysis, Berlin, 1990, Lecture Notes in Math. 1481 Springer Berlin (1990), 97-103. MR 1178522 |
| 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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[Tr] Tricerri F.: Locally homogeneous Riemannian manifolds.Rend. Sem. Mat. Univ. Politec. Torino 50/4 (1993), 411-426. Zbl 0804.53072, MR 1261452 |
| Reference:
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| Reference:
|
[TW] Tricerri F., Watanabe Y.: Infinitesimal models and locally homogeneous almost Hermitian manifolds.Math. J. Toyama Univ. 18 (1995), 147-154. Zbl 0865.53042, MR 1369702 |
| . |
