Object's details: A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds

Provider:Akademicka Platforma Czasopism

Description

Title:
A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
Creator:
Musso, Monica;
Pejsachowicz, Jacobo;
Portaluri, Alessandro
Description:
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 our generalized 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.
Object availability:
free access
Rights:
Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
Date:
2005.03.01
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 25, No 1 (March 2005); 69 - 99;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.004/9256
Subject:
Perturbed geodecics;
semi-Riemannian manifold;
spectral flow;
conjugate points;
generalized Morse index;
37G25;
37J05;
47A07;
47A53;
53C22;
53C50;
58E10
Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.004
Data provider:
Akademicka Platforma Czasopism

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