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September 2007 Complex hyperpolar actions with a totally geodesic orbit
Naoyuki Koike
Osaka J. Math. 44(3): 491-503 (September 2007).

Abstract

We first show that homogeneous submanifolds with abelian normal bundle in a symmetric space of non-compact type occur as principal orbits of complex hyperpolar actions on the symmetric space. Next we show that all complex hyperpolar actions with a reflective orbit are orbit equivalent to Hermann type actions. Furthermore, we classify complex hyperpolar actions with a totally geodesic orbit in the case where the ambient symmetric space is irreducible. Also, we list up the cohomogeneities of Hermann type actions on irreducible symmetric spaces.

Citation

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Naoyuki Koike. "Complex hyperpolar actions with a totally geodesic orbit." Osaka J. Math. 44 (3) 491 - 503, September 2007.

Information

Published: September 2007
First available in Project Euclid: 13 September 2007

zbMATH: 1146.53031
MathSciNet: MR2360937

Subjects:
Primary: 53C35
Secondary: 53C40

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
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Vol.44 • No. 3 • September 2007
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