# 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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