Title:
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Einstein-like semi-symmetric spaces (English) |
Author:
|
Boeckx, E. |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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29 |
Issue:
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2 |
Year:
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1993 |
Pages:
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235-240 |
Summary lang:
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English |
. |
Category:
|
math |
. |
Summary:
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One proves that semi-symmetric spaces with a Codazzi or Killing Ricci tensor are locally symmetric. Some applications of this result are given. (English) |
Keyword:
|
semi-symmetric spaces |
Keyword:
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Killing and Codazzi Ricci tensor |
Keyword:
|
locally symmetric spaces |
Keyword:
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spaces with volume-preserving geodesic symmetries |
Keyword:
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C-spaces |
Keyword:
|
Osserman spaces |
MSC:
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53C25 |
MSC:
|
53C35 |
idZBL:
|
Zbl 0807.53041 |
idMR:
|
MR1263125 |
. |
Date available:
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2008-06-06T21:25:08Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107486 |
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Reference:
|
[BPV] Berndt, J., Prüfer, F., Vanhecke, L.: Symmetric-like Riemannian manifolds and geodesic symmetries.preprint. MR 1331561 |
Reference:
|
[BV] Berndt, J., Vanhecke, L.: Two natural generalizations of locally symmetric spaces.Diff. Geom. Appl. 2 (1992), 57-80. MR 1244456 |
Reference:
|
[B] Besse, A. L.: Einstein manifolds.Ergeb. Math. Grenzgeb. 3. Folge 10, Springer-Verlag, Berlin, Heidelberg, New York, 1987. Zbl 1147.53001, MR 0867684 |
Reference:
|
[Bo] Boeckx, E.: Asymptotically foliated semi-symmetric spaces.in preparation. Zbl 0846.53031 |
Reference:
|
[BKV] Boeckx, E., Kowalski, O., Vanhecke, L.: Non-homogeneous relatives of symmetric spaces.Diff. Geom. Appl. (to appear). |
Reference:
|
[Ca] Cartan, E.: Leçons sur la géométrie des espaces de Riemann.2nd edition, Paris, 1946. Zbl 0060.38101, MR 0020842 |
Reference:
|
[Ch] Cho, J. T.: Natural generalizations of locally symmetric spaces.Indian J. Pure Appl. Math. (to appear). Zbl 0772.53029, MR 1218533 |
Reference:
|
[D’AN] D’Atri, J. E., Nickerson, H. K.: Divergence-preserving geodesic symmetries.J. Diff. Geom. 3 (1969), 467-476. MR 0262969 |
Reference:
|
[GSV] Gilkey, P., Swann, A., Vanhecke, L.: Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator.preprint. MR 1348819 |
Reference:
|
[G] Gray, A.: Einstein-like manifolds which are not Einstein.Geom. Dedicata 7 (1978), 259-280. Zbl 0378.53018, MR 0505561 |
Reference:
|
[KN] Kobayashi, S., Nomizu, K.: Foundations of differential geometry I, II.Interscience Publishers, New York, 1963, 1969. MR 0152974 |
Reference:
|
[K1] Kowalski, O.: Spaces with volume-preserving geodesic symmetries and related classes of Riemannian manifolds.Rend. Sem. Mat. Univ. Politec. Torino, Fascicolo Speciale Settembre (1983), 131–158. MR 0829002 |
Reference:
|
[K2] Kowalski, O.: An explicit classification of 3-dimensional Riemannian spaces satisfying $\scriptstyle R(X,Y)\cdot R=0$.preprint. MR 1408298 |
Reference:
|
[O] R. Osserman: Curvature in the eighties.Amer. Math. Monthly 97 (1990), 731-756. Zbl 0722.53001, MR 1072814 |
Reference:
|
[S] Sinjukov, N. S.: Geodesic maps on Riemannian spaces.(Russian), Publishing House “Nauka" Moscow, 1979. MR 0552022 |
Reference:
|
[Sz1] Szabó, Z. I.: Structure theorems on Riemannian manifolds satisfying $\scriptstyle R(X,Y)\cdot R=0$, I,Local version.J. Diff. Geom. 17 (1982), 531-582. MR 0683165 |
Reference:
|
[Sz2] Szabó, Z. I.: Structure theorems on Riemannian manifolds satisfying $\scriptstyle R(X,Y)\cdot R=0$, II, Global versions.Geom. Dedicata 19 (1985), 65-108. MR 0797152 |
Reference:
|
[V1] Vanhecke, L.: Some solved and unsolved problems about harmonic and commutative spaces.Bull. Soc. Math. Belg., Sér. B 34 (1982), 1-24. Zbl 0518.53042, MR 0683378 |
Reference:
|
[V2] Vanhecke, L.: Geometry in normal and tubular neighborhoods.Lecture Notes, Proc. Workshop on Differential Geometry and Topology, Cala Gonone (Sardinia), Rend. Sem. Fac. Sci. Univ. Cagliari, Supplemento al Vol. 58 (1988), 73-176. MR 1122858 |
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