The Maslov index and a generalized Morse index theorem for non-positive definite metrics

We present an extension of the celebrated Morse index theorem in Riemannian geometry to the case of geodesics in pseudo-Riemannian manifolds. It is co nsidered the case that both endpoints are variable. The notion of Maslov in dex for pseudo-Riemannian geodesics replaces the notion of geometric index for Riemannian geodesics. (C) 2000 Academie des sciences/Editions scientifi ques et medicales Elsevier SAS.