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
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2906
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2014-08)
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