Opis

• Tytuł:
  A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• Twórca:
  Musso, Monica;
  Pejsachowicz, Jacobo;
  Portaluri, Alessandro
• Opis:
  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.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2005.03.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 25, No 1 (March 2005); 69 - 99;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.004/9256
• Temat i słowa kluczowe:
  Perturbed geodecics;
  semi-Riemannian manifold;
  spectral flow;
  conjugate points;
  generalized Morse index;
  37G25;
  37J05;
  47A07;
  47A53;
  53C22;
  53C50;
  58E10
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.004
• Dostawca danych:
  Akademicka Platforma Czasopism
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