Abstract

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Keywords

Maslov index, geodesics, semi-Riemannian geometry, conjugate points, focal points

Mathematical Subject Classification

Primary: 53C22, 53C50, 53D12, 53D25

Milestones

Received: 1 October 2008
Revised: 13 February 2009
Accepted: 11 April 2009

Authors