Comparison results for conjugate and focal points in semi-Riemannian geometry via Maslov index

Miguel Ángel Javaloyes and Paolo Piccione

Vol. 243 (2009), No. 1, 43–56

DOI: 10.2140/pjm.2009.243.43

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 2000

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

Milestones

Received: 1 October 2008

Revised: 13 February 2009

Accepted: 11 April 2009

Published: 1 November 2009