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On Totally Geodesic Surfaces in Symmetric Spaces of Type AI

  • Takuya Fujimaru
  • Akira Kubo
  • Hiroshi Tamaru
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)

Abstract

We develop an approach to the classification of nonflat totally geodesic surfaces in Riemannian symmetric spaces of noncompact type. In this paper, we concentrate on the case of symmetric spaces of type AI, and show that such surfaces correspond to certain nilpotent matrices. As applications, we obtain explicit classifications in the cases of rank two and three.

Keywords

Symmetric Space Sectional Curvature Riemannian Symmetric Space Iwasawa Decomposition Cartan Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors would like to thank Yoshio Agaoka, Katsuya Mashimo, and Takayuki Okuda for useful comments and discussions. The third author was supported in part by KAKENHI (24654012).

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsHigashi-HiroshimaJapan
  2. 2.Usuki High SchoolUsukiJapan

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