Abstract
The singular set Ξ for a manifoldM with a smooth, symmetric two-tensorg is defined to be the set of points of degeneracy for the two-tensorg. The main results of this paper are an existence and uniqueness theorem for geodesics through the singular set and existence and uniqueness theorems for parallel and Jacobi fields along these geodesics. These theorems apply to semi-Riemannian submanifold geometry, where the metric induced on a submanifold of an ambient semi-Riemannian manifold may degenerate.
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Part of this research was supported by a grant from the Danish Research Academy and this gave the author the opportunity to visit the Mathematics Institute at University of Warwick in the fall 1990. The author is grateful to the members of the staff for many interesting discussions during the author’s pleasant stay.
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Larsen, J.C. Submanifold geometry. J Geom Anal 4, 179–205 (1994). https://doi.org/10.1007/BF02921546
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DOI: https://doi.org/10.1007/BF02921546