Osaka Journal of Mathematics

Complex hyperpolar actions with a totally geodesic orbit

Naoyuki Koike

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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.

Article information

Osaka J. Math., Volume 44, Number 3 (2007), 491-503.

First available in Project Euclid: 13 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C35: Symmetric spaces [See also 32M15, 57T15]
Secondary: 53C40: Global submanifolds [See also 53B25]


Koike, Naoyuki. Complex hyperpolar actions with a totally geodesic orbit. Osaka J. Math. 44 (2007), no. 3, 491--503.

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