Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Abstract | References | Similar Articles | Additional Information

Abstract: Examples of Osserman pseudo-Riemannian manifolds with metric of any signature $(p,q)$, $p$, $q$ $>1$ which are not locally symmetric are exhibited.

References [Enhancements On Off] (What's this?)

  • [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).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53B30, 53C50

Retrieve articles in all journals with MSC (1991): 53B30, 53C50

Additional Information

E. García-Río
Affiliation: Departamento de Análise Matemática, Facultade de Matemáticas, 15706 Santiago de Compostela, Spain

M. E. Vázquez-Abal
Affiliation: Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, 15706 Santiago de Compostela, Spain

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

American Mathematical Society