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 ...

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 ...

Let X, Y be asymmetric normed spaces and Lc(X, Y ) the convex cone of all linear continuous operators from X to Y . It is known that in general, Lc(X, Y ) is not a vector space. The aim of this note is to give, using ...

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 ...

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 ...

The long-term sustainability of space activities is an emerging issue to which actors in the global space community –including governments, agencies, and industry– are devoting increasing amounts of attention and resources. ...

Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a (non-trivial) totally geodesic submanifold of M. The purpose of this note is to determine the index i(M) for all ...

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, ...