Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T12:34:31.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized pointwise symmetric Riemannian spaces: a classification

Published online by Cambridge University Press:  24 October 2008

R. A. Marinosci
R. A. Marinosci
Affiliation:
Dipartimento di Matematica, Università di Lecce, Italy
Get access Rights & Permissions [Opens in a new window]

Extract

The theory of generalized symmetric spaces was begun by P. J. Graham and A. J. Ledger in 1967 in their paper [1]. Other authors who contributed to this topic were, e.g. F. Brickel, A. Deicke, A. S. Fedenko, A. Gray, V. G. Kac, M. Obata, B. Pettit, K. Sekigawa and J. Wolf; more recently also J. A. Jiménez, A. R. Razawi, C. Sánchez, M. Sekizawa, M. Toomanian, G. Tsagas and L. Vanhecke. A systematic exposition is given in the book by O. Kowalski[3, 4]. The author classifies all generalized symmetric Riemannian spaces in dimension n ≤ 5, using a systematic method.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 3 , November 1988 , pp. 505 - 520
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Graham, P. J. and Ledger, A. J.. Sur une classe de s-variétés riemannianes ou affines. C. R. Acad. Sci. Paris Sér I Math. 267 (1967), 947–948.Google Scholar
[2]Kobayashi, S. and Nomizu, K.. Foundations of Differential Geometry (Interscience, vol. I (1963), vol. II (1969)).Google Scholar
[3]Kowalski, O.. Generalized Symmetric Spaces. Lecture Notes in Math. vol. 805 (Springer-Verlag, 1980).Google Scholar
[4]Kowalski, O.. Generalized Symmetric Spaces, revised Russian version (MIR, 1984).Google Scholar
[5]Kowalski, O.. Classification of generalized symmetric Riemannian spaces of dimension n ≤ 5. Rozpravy Československé Acad. Věd. Řada Mat. Přírod. Věd. 85 (1975), 61.Google Scholar
[6]Nomizu, K.. Invariant affine connections on homogeneous spaces. Amer. J. Math. 76 (1954), 33–65.Google Scholar