On some methods of construction of invariant normalizations of lightlike hypersurfaces
| dc.creator | Akivis, Maks A. | |
| dc.creator | Goldberg, Vladislav V. | |
| dc.date | 1999-02-08 | |
| dc.date.accessioned | 2026-07-07T05:27:51Z | |
| dc.date.available | 2026-07-07T05:27:51Z | |
| dc.description | The authors study the geometry of lightlike hypersurfaces on pseudo-Riemannian manifolds $(M, g)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. For a lightlike hypersurface $V \subset (M, g)$ of general type and for some special lightlike hypersurfaces (namely, for totally umbilical and belonging to a manifold $(M, g)$ of constant curvature), in a third-order neighborhood of a point $x \in V$, the authors construct invariant normalizations intrinsically connected with the geometry of $V$ and investigate affine connections induced by these normalizations. For this construction, they used relative and absolute invariants defined by the first and second fundamental forms of $V$. The authors show that if $\dim M = 4$, their methods allow to construct three invariant normalizations and affine connections intrinsically connected with the geometry of $V$. Such a construction is given in the present paper for the first time. The authors also consider the fibration of isotropic geodesics of $V$ and investigate their singular points and singular submanifolds. | |
| dc.description | LaTeX, 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/9902056 | |
| dc.identifier | http://arxiv.org/abs/math/9902056 | |
| dc.identifier | Differential Geom. Appl., 12 (2000) no. 2 121-143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78079 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B25, 53B20, 53B21, 53B30 | |
| dc.title | On some methods of construction of invariant normalizations of lightlike hypersurfaces | |
| dc.type | text |