Lightlike submanifolds of semi-Riemannian manifolds. (English) Zbl 0831.53040
This paper initiates a general study of arbitrary lightlike (degenerate) submanifolds of semi-Riemannian manifolds. The authors construct the canonical lightlike transversal vector bundle of a lightlike submanifold with respect to a given screen distribution on it. Four cases are studied with respect to the degree of nullity of the lightlike submanifold and examples are given. The induced geometric structure on lightlike submanifolds is studied and the authors show that the leaves of the vertical vector bundle are totally geodesically immersed as lightlike submanifolds of the tangent bundle with a semi-Riemannian metric, and that lightlike immersions are affine immersions in the sense of Nomizu and Pinkall.
Reviewer: B.Rouxel (Quimper)
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
Keywords:
degenerate metric; second fundamental form; totally geodesic immersions; lightlike submanifoldReferences:
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