Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-18T18:54:01.536Z Has data issue: false hasContentIssue false
  • English
  • Français

An example of rank two symmetric Osserman space

Published online by Cambridge University Press:  17 April 2009

Zoran Rakić
Zoran Rakić
Affiliation:
Faculty of MathematicsUniversity of BelgradeStudentski Trg 16, P.P. 55011000 BelgradeYugoslavia e-mail: xpmfm28@yubgss21.bg.ac.yu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently, Blažić, Bokan and Rakić, obtained some classes of 4-dimensional Osserman pseudo-Riemannian manifolds. One of these is the class of rank 2 locally symmetric space endowed with an integrable para-quaternionic structure. In this paper we give an explicit construction of an example of a space of that kind.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 517 - 521
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Blažić, N., Bokan, N. and Rakič, Z., ‘Characterization of 4-dimensional Osserman pseudo-Riemannian Manifolds’, (preprint).Google Scholar
[2]Chi, Q.S., ‘A curvature characterization of certain locally rank-one symmetric spaces’, J. Differential Geom. 28 (1988), 187–202.CrossRefGoogle Scholar
[3]Chi, Q.S., ‘Curvature characterization and classification of rank-one symmetric spaces’, Pacific. J. Math. 150 (1991), 31–42.CrossRefGoogle Scholar
[4]Gilkey, P.B., Swann, A. and Vanhecke, L., ‘Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator’, Quart. J. Math. Oxford. 46 (1995), 299–320.CrossRefGoogle Scholar
[5]Osserman, R., ‘Curvature in the eighties’, Amer. Math. Monthly 97 (1990), 731–756.CrossRefGoogle Scholar
[6]Postnikov, M.M., Lectures in geometry; Lie groups and Lie algebras, (English translation) (Mir Publishers, Moskva, 1986).Google Scholar
[7]Wu, H., ‘Holonomy groups of indefinite metrics’, Pacific. J. Math. 20 (1967), 351–392.CrossRefGoogle Scholar