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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
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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

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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