Submanifold geometry

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jun 1994 English Publisher:Springer Science and Business Media LLCJournal:Journal of Geometric Analysis, volume 4, pages 179-205 (issn: 1050-6926, eissn: 1559-002X,

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Authors: Larsen, Jens Chr.;

doi: 10.1007/bf02921546

Submanifold geometry

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Abstract

Let \(M\) be a manifold endowed with a symmetric tensor field \(g\) of type \((0,2)\). Denote by \(S\) the set of points of degeneracy for \(g\). The author obtains an existence and uniqueness theorem for geodesics through \(S\) and existence and uniqueness theorems for parallel and Jacobi fields along these geodesics.

Related Organizations

Technical University of Denmark
Denmark

Keywords

Local differential geometry of Lorentz metrics, indefinite metrics, geodesic Jacobi field, singular set, Geodesics in global differential geometry, semi-Riemannian manifold

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