A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds

Details A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds

2003-11-10

arxiv.org/abs/math/0311147v2

Mathematics

Differential Geometry

32 pages. LaTex2e.No figures. Some minor changes

Scientific paper

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. We also introduce a new counting for conjugate points, which need not to be isolated in this context, and prove that the relative Morse index equals the total number of conjugate points. Finally we study the relation with the Maslov index of the flow induced on the Lagrangian Grassmannian.

Affiliated with

Also associated with

No associations

Rating

A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-51195