Distances of Polars in Pointed Symmetric R-Spaces
- Polars in a pointed compact symmetric space are connected components of the fixed point set of the geodesic symmetry at the origin. They carry important information about the ambient symmetric space. In this note we show that the distances to the origin of two distinct polars in a pointed indecomposable symmetric R-space are different. August 4, 2015; Note added by the authors: A referee kindly informed us that the main result of this preprint, Theorem 1, can also be deduced from the pages 24 and 26 of the following article: M. Takeuchi, On conjugate loci and cut loci of compact symmetric spaces II, Tsukuba J. Math. 3, 1-29 (1979)
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| Author: | Peter QuastGND, Makiko Sumi Tanaka |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-29061 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2906 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2014-08) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2014/11/21 |
| Tag: | symmetric R-space; totally geodesic submanifold; polar; hermitian symmetric space |
| GND-Keyword: | Polare; Hermitescher symmetrischer Raum; Riemannsche Geometrie |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
