The property of geodesic invariance of a distribution on a manifold with an affine connection is that for which geodesics with initial tangent vectors in the distribution are such that all subsequent tangent vectors are in the distribution. The symmetric product is the infinitesimal measure of geodesic invariance. In the talk, the manner in which these notions arise in various areas will be illustrated.

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Last Updated: Fri Apr 25 10:29:10 2025