Tsukuba Journal of Mathematics

Stability of Certain Reflective Submanifolds in Compact Symmetric Spaces

Taro Kimura

Full-text: Open access

Abstract

In [1], J. Berndt and H. Tamaru classified all the cohomogeneity one actions on Riemannian symmetric spaces of noncompact type with a totally geodesic singular orbit. Also they provided that there is a one-to-one correspondence between the totally geodesic singular orbits of cohomogeneity one actions on a Riemannian symmetric space of noncompact type and those on its dual simply connected compact Riemannian symmetric space. In this paper, we determine stability of the totally geodesic singular orbits in simply connected compact symmetric spaces which obtained by the duality stated above.

Article information

Source
Tsukuba J. Math., Volume 32, Number 2 (2008), 361-382.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165236

Digital Object Identifier
doi:10.21099/tkbjm/1496165236

Mathematical Reviews number (MathSciNet)
MR2477987

Zentralblatt MATH identifier
1168.53027

Citation

Kimura, Taro. Stability of Certain Reflective Submanifolds in Compact Symmetric Spaces. Tsukuba J. Math. 32 (2008), no. 2, 361--382. doi:10.21099/tkbjm/1496165236. https://projecteuclid.org/euclid.tkbjm/1496165236


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