Remarks on the generalized Hestenes's lemma

摘要

Suppose we have an m-jet field on a set V subset of R-n (with subset S) which is a Whitney field on V - S. We study two metric invariants q and l which relate in different ways the geodesic and Euclidean distances on V. We prove that, if the field is at least as flat as mq/l at S, then it is a Whitney field on V. When V is subanalytic, q and l are finite.