Totally Geodesic Submanifolds of Riemannian Symmetric Spaces

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


The index of a Riemannian manifold is defined as the minimal codimension of a totally geodesic submanifold. In this note we discuss two recent results by the author and Olmos (Berndt and Olmos, On the index of symmetric spaces, preprint, arXiv:1401.3585) and some related topics. The first result states that the index of an irreducible Riemannian symmetric space is bounded from below by the rank of the symmetric space. The second result is the classification of all irreducible Riemannian symmetric spaces of noncompact type whose index is less or equal than three.


Riemannian Manifold Symmetric Space Maximal Dimension Isotropy Representation Riemannian Symmetric Space 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUK

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