info:eu-repo/semantics/article
The index of symmetry of compact naturally reductive spaces
Fecha
2014-08Registro en:
Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; Tamaru, Hiroshi; The index of symmetry of compact naturally reductive spaces; Springer; Mathematische Zeitschrift; 277; 3-4; 8-2014; 611-628
0025-5874
CONICET Digital
CONICET
Autor
Olmos, Carlos Enrique
Reggiani, Silvio Nicolás
Tamaru, Hiroshi
Resumen
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 reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold