On the index of symmetric spaces

Jurgen Berndt, Carlos Olmos

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
154 Downloads (Pure)


Let M be an irreducible Riemannian symmetric space. The index of M is the minimal codimension of a (non-trivial) totally geodesic submanifold of M. We prove that the index is bounded from below by the rank of the symmetric space. We also classify the irreducible Riemannian symmetric spaces whose index is less or equal than 3.
Original languageEnglish
Pages (from-to)33-48
Number of pages16
JournalJournal fur die Reine und Angewandte Mathematik
Early online date13 Oct 2015
Publication statusPublished - 1 Apr 2018


  • symmetric spaces
  • totally geodesic submanifolds
  • index of symmetric spaces


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