The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold. There is a conjecture for how to calculate the index. In this paper we give an affirmative answer to this ...

This paper studies structural properties of locally symmetric submanifolds. One of the main result states that a locally symmetric submanifold M of R-n admits a locally symmetric tangential parametrization in an appropriately ...

Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved that i(M) is bounded from below by the rank rk(M) of M, that is, ...

Let M be an irreducible Riemannian symmetric space. The indexof M is the minimal codimension of a (non-trivial) totally geodesic submanifoldof M. We prove that the index is bounded from below by the rank ofthe symmetric ...

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In ...

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. ...

We give the symmetric version of five lemmas which are essential for the theory of tensor products (and norms). These are: the approximation, extension, embedding, density and local technique lemma. Some applications of ...

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally ...

We study 'H POT.1' versus 'C POT.1' local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of O(N). These functionals, in many cases, ...