Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

摘要: We study the singularities of exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues curvature tensor, and their contribution to Maslov index geodesic is computed explicitly. prove that degeneracy conjugate points, which a phenomenon can occur semi-Riemannian geometry, caused case by lack diagonalizability tensor. The Lie groups endowed with bi-invariant metric studied some detail, conditions are given for local injectivity around its singularities.