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Reflections and symmetries in compact symmetric spaces

Published online by Cambridge University Press:  17 April 2009

Bang-Yen Chen  and
Lieven Vanhecke
Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States of America
Lieven Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3030 Leuven, Belgium
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Abstract

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Point symmetries and reflections are two important transformations on a Riemannian manifold. In this article we study the interactions between point symmetries and reflections in a compact symmetric space when the reflections are global isometries.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 377 - 386
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Chen, B.Y., A new approach to compact symmetric spaces and applications: a report on joint work with Professor T. Nagano (Katholieke Universiteit Leuven, 1987).Google Scholar
[2]Chen, B.Y. and Nagano, T., ‘Totally geodesic submanifolds of symmetric spaces, I, II’, Duke Math. J. 44 (1977), 745–755; 45 (1978) 405–425.CrossRefGoogle Scholar
[3]Chen, B.Y. and Nagano, T., ‘A Riemannian geometric invariant and its applications to a problem of Borel and Serre’, Trans. Amer. Math. Soc. 308 (1988).CrossRefGoogle Scholar
[4]Chen, B.Y. and Vanhecke, L., ‘Isometric, holomorphic and symplectic reflections’, Geometriae Dedicata. (to appear)Google Scholar
[5]Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces (Academic Press, New York, 1978).Google Scholar
[6]Kobayaski, S. and Nomizu, K., Foundations of Differential Geometry, vol II (Interscience Publishers, 1969).Google Scholar
[7]Nagano, T., ‘The involutions of compact symmetric spaces’ (to appear).Google Scholar