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}
}
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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