Maximal totally geodesic submanifolds and index of symmetric spaces

• Autores: Berndt, Jürgen; Olmos, Carlos Enrique
• Año de publicación: 2016
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: totally geodesic submanifolds; symmetric spaces
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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, rk(M) ≤ i(M). In this paper we classify all irreducible Riemannian symmetric spaces M for which the equality holds, that is, rk(M) = i(M). In this context we also obtain an explicit classification of all non-semisimple maximal totally geodesic submanifolds in irreducible Riemannian symmetric spaces of noncompact type and show that they are closely related to irreducible symmetric R-spaces. We also determine the index of some symmetric spaces and classify the irreducible Riemannian symmetric spaces of noncompact type with i(M) ∈ {4, 5, 6}.
Fil: Berndt, Jürgen. King's College London; Reino Unido
Fil: Olmos, Carlos Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina