Pseudo focal points along Lorentzian geodesics and Morse index
| dc.creator | Javaloyes, Miguel Angel | |
| dc.creator | Masiello, Antonio | |
| dc.creator | Piccione, Paolo | |
| dc.date | 2007-11-19 | |
| dc.date | 2009-04-20 | |
| dc.date.accessioned | 2026-07-07T13:05:25Z | |
| dc.date.available | 2026-07-07T13:05:25Z | |
| dc.description | Given a Lorentzian manifold $(M,g)$, a geodesic $γ$ in $M$ and a timelike Jacobi field $\mathcal Y$ along $γ$, we introduce a special class of instants along $γ$ that we call $\mathcal Y$-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the $\mathcal Y$-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 $\mathcal Y$ is obtained as the restriction of a globally defined timelike Killing vector field. | |
| dc.description | 26 pages, Proposition 3.10, that has become Proposition 3.11 in the current version, has changed introducing a new class of points that we call pseudo-focal points. The new Section 5 is devoted to describe some properties to these points | |
| dc.identifier | https://arxiv.org/abs/0711.3032 | |
| dc.identifier | http://arxiv.org/abs/0711.3032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227480 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B30, 53C22, 58E05 | |
| dc.title | Pseudo focal points along Lorentzian geodesics and Morse index | |
| dc.type | text |