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Nonsymmetric Osserman pseudo-Riemannian manifolds
Author(s):
E.
García-Río;
M.
E.
Vázquez-Abal;
R.
Vázquez-Lorenzo
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2771-2778.
MSC (1991):
Primary 53B30, 53C50
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Abstract:
Examples of Osserman pseudo-Riemannian manifolds with metric of any signature  ,  ,   which are not locally symmetric are exhibited.
References:
- [1]
- M. Barros and A. Romero, Indefinite Kähler manifolds, Math. Ann. 261 (1982), 55-62.MR 84d:53033
- [2]
- N. Bla\v{z}i\'{c}, N. Bokan and P. Gilkey, A Note on Osserman Lorentzian manifolds, Bull. London Math. Soc. 29 (1997), 227-230. MR 97m:53111
- [3]
- Q.S. Chi, A curvature characterization of certain locally rank-one symmetric spaces, J. Diff. Geom. 28 (1988), 187-202. MR 90a:53060
- [4]
- Q.S. Chi, Quaternionic Kähler manifolds and a characterization of two-point homogeneous spaces, Illinois J. Math. 35 (1991), 408-418.MR 92f:53051
- [5]
- Q.S. Chi, Curvature characterization and classification of rank-one symmetric spaces, Pacific J. Math. 150 (1991), 31-42. MR 92g:53044
- [6]
- P.M. Gadea and A. Montesinos Amilibia, Spaces of constant paraholomorphic sectional curvature, Pacific J. Math. 136 (1989), 85-101.MR 90d:53043
- [7]
- E. García-Río and D. N. Kupeli, Four-dimensional Osserman Lorentzian manifolds, New Developments in Differential Geometry (L. Tamássy and J. Szenthe, eds.), Kluwer Acad. Publ., 1996, pp. 201-211. MR 97d:53067
- [8]
- E. García-Río, D. N. Kupeli and M. E. Vázquez-Abal, On a problem of Osserman in Lorentzian geometry, Diff. Geom. Appl. 7 (1997), 85-100.CMP 97:10
- [9]
- P. Gilkey, A. Swann and L. Vanhecke, Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator, Quart. J. Math. Oxford 46 (1995), 299-320. MR 96h:53051
- [10]
- B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.MR 85f:53002
- [11]
- R. Osserman, Curvature in the eighties, Amer. Math. Monthly 97 (1990), 731-756. MR 91i:53001
- [12]
- Z. Raki\'{c}, Rank-2 symmetric Osserman spaces, Bull. Austr. Math. Soc. (to appear).
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Additional Information:
E.
García-Río
Affiliation:
Departamento de Análise Matemática, Facultade de Matemáticas, 15706 Santiago de Compostela, Spain
Email:
eduardo@zmat.usc.es
M.
E.
Vázquez-Abal
Affiliation:
Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, 15706 Santiago de Compostela, Spain
Email:
meva@zmat.usc.es
R.
Vázquez-Lorenzo
Affiliation:
Facultade de Matemáticas, 15706 Santiago de Compostela, Spain
DOI:
10.1090/S0002-9939-98-04666-8
PII:
S 0002-9939(98)04666-8
Keywords:
Jacobi operator,
Osserman space,
pseudo--Riemannian metric
Received by editor(s):
January 30, 1997
Additional Notes:
Supported by projects DGICYT PB940633C0201 and XUGA 20702B96, Spain.
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1998,
American Mathematical Society
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