Description

• Title:
  Genericity of nondegenerate geodesics with general boundary conditions
• Creator:
  Bettiol, Renato G.;
  Giambò, Roberto
• Description:
  Let $M$ be a possibly noncompact manifold. We prove, generically in the $C^k$-topology ($2\leq k\leq \infty$), that semi-Riemannian metrics of a given index on $M$ do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [< i> Genericity of nondegenerate critical points and Morse geodesic functionals< /i> , Indiana Univ. Math. J. < b> 58< /b> (2009), 1797–1830] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold $\mathcal P\subset M\times M$ that satisfies an admissibility condition. Such condition holds, for example, when $\mathcal P$ is transversal to the diagonal $\Delta\subset M\times M$. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are $C^k$-generic are given.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 2 (June 2010); 339 - 365;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.020/8465
• Subject:
  Generic properties;
  semi-Riemannian geodesic flows;
  nondegenerate geodecics;
  general endpoints conditions;
  57R45;
  57R70;
  57N75;
  58E10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.020
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other