On the Geodesical Connectedness for a Class of Semi-Riemannian Manifolds

We prove a variational principle for geodesics on a semi-Riemannian manifold M of arbitrary index k and possessing k linearly independent Killing vector fields that generate a timelike distribution on M. Using such a principle and a suitable completeness condition for M, we prove some existence and...

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Veröffentlicht in:	Journal of mathematical analysis and applications 2000-12, Vol.252 (1), p.444-476
Hauptverfasser:	Giannoni, Fabio, Piccione, Paolo, Sampalmieri, Rosella
Format:	Artikel
Sprache:	eng
Schlagworte:	Differential geometry Exact sciences and technology Functions of a complex variable geodesics Geometry Ljusternik–Schnirelman theory Mathematical analysis Mathematics Palais–Smale condition Sciences and techniques of general use semi-Riemannian geometry
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Beschreibung
Zusammenfassung:	We prove a variational principle for geodesics on a semi-Riemannian manifold M of arbitrary index k and possessing k linearly independent Killing vector fields that generate a timelike distribution on M. Using such a principle and a suitable completeness condition for M, we prove some existence and multiplicity results for geodesics joining two fixed points of M.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.2000.7103