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Nonsymmetric Osserman
pseudo-Riemannian manifolds
Authors:
E. García-Río, M. E. Vázquez-Abal and R. Vázquez-Lorenzo
Journal:
Proc. Amer. Math. Soc. 126 (1998), 2771-2778
MSC (1991):
Primary 53B30, 53C50
MathSciNet review:
1476128
Full-text PDF Free Access
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Additional Information
Abstract: Examples of Osserman pseudo-Riemannian manifolds with metric of any signature  ,  ,   which are not locally symmetric are exhibited.
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- [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
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- 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
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- 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
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- B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.MR 85f:53002
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- R. Osserman, Curvature in the eighties, Amer. Math. Monthly 97 (1990), 731-756. MR 91i:53001
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- 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
DOI:
http://dx.doi.org/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
Article copyright:
© Copyright 1998 American Mathematical Society
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