Osaka Journal of Mathematics

Complex hyperpolar actions with a totally geodesic orbit

Naoyuki Koike

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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.

Article information

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

Dates
First available in Project Euclid: 13 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1189717419

Mathematical Reviews number (MathSciNet)
MR2360937

Zentralblatt MATH identifier
1146.53031

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

Citation

Koike, Naoyuki. Complex hyperpolar actions with a totally geodesic orbit. Osaka J. Math. 44 (2007), no. 3, 491--503. https://projecteuclid.org/euclid.ojm/1189717419


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