Artículos de revistas
Pseudo Focal Points Along Lorentzian Geodesics and Morse Index
Fecha
2010Registro en:
ADVANCED NONLINEAR STUDIES, v.10, n.1, p.53-82, 2010
1536-1365
Autor
JAVALOYES, Miguel Angel
MASIELLO, Antonio
PICCIONE, Paolo
Institución
Resumen
Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.