# A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds

@article{Musso2005AMI,
title={A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds},
author={Monica Musso and Jacobo Pejsachowicz and Alessandro Portaluri},
journal={Topological Methods in Nonlinear Analysis},
year={2005},
volume={25},
pages={69-99}
}
• Published 1 March 2005
• Mathematics
• Topological Methods in Nonlinear Analysis
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-Riemannian manifolds the well known Morse Index Theorem. When the metric is indefinite, the Morse index of the energy functional becomes infinite and hence, in order to obtain a meaningful statement, we substitute the Morse index by its relative form, given by the spectral flow of an associated family of index forms…
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