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- W2952531760 abstract "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." @default.
- W2952531760 created "2019-06-27" @default.
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- W2952531760 date "1999-02-08" @default.
- W2952531760 modified "2023-09-27" @default.
- W2952531760 title "On some methods of construction of invariant normalizations of lightlike hypersurfaces" @default.
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