Advertisement

Totally Geodesic Surfaces of Riemannian Symmetric Spaces

  • Katsuya Mashimo
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)

Abstract

A submanidfold S of a Riemannian manifold is called a totally geodesic submanifold if every geodesic of S is also a geodesic of M. Totally geodesic submanifolds of Riemannian symmetric spaces have long been studied by many mathematicians. We give a classification of non-flat totally geodesic surfaces of the Riemannian symmetric space of type AI, AIII and BDI.

Keywords

Irreducible Representation Riemannian Symmetric Space Geodesic Submanifold Involutive Automorphism Standard Orthonormal Basis 
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.

References

  1. 1.
    Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic press, New York (1978)MATHGoogle Scholar
  2. 2.
    Klein, S.: Totally Geodesic Submanifolds in Riemannian Symmetric Spaces. arXiv:0810.4413v1 [math.DG]Google Scholar
  3. 3.
    Mashimo, K.: Non-flat Totally Geodesic Surfaces in Symmetric Spaces of Classical Type. PreprintGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Hosei universityTokyoJapan

Personalised recommendations