Pseudo-Riemannian metric singularities and the extendability of parallel transport
Author: Marek Kossowski
Journal: Proc. Amer. Math. Soc. 99 (1987), 147-154
MSC: Primary 53C50; Secondary 53C40, 58A12
MathSciNet review: 866445
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Abstract: We are given a immersion , and is a point where is one-dimensional. We have shown that there is a tensor intrinsic to which determines an extrinsic feature of the immersion. The purpose of this paper is to show that II controls the following two intrinsic properties. First, II determines which pairs of vector fields , on have the property that intrinsic covariant derivative extends smoothly to all of . Second, given a curve in containing determines which parallel vector fields along the curve extend smoothly through . As an application we locally characterize product and flat metric singularities.
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