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

TL;DR

This paper establishes an estimate for the Maslov index difference based on reference Lagrangians and explores its applications to conjugate and focal points in semi-Riemannian geometry.

Contribution

It introduces a new estimate for the Maslov index difference and applies it to analyze conjugate and focal points along geodesics in semi-Riemannian manifolds.

Findings

Derived an estimate for Maslov index differences based on reference Lagrangians.

Applied the estimate to study conjugate points in semi-Riemannian geometry.

Provided insights into the behavior of focal points along geodesics.

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.