High-jet relations of the heat kernel embedding map and applications

2013/08/02 by Ke Zhu, Zhu, Ke
Mathematics · #53C42 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP #msc:53C42 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1308.0410

28 pages, related references on random functions are added

arxiv created 2013/08/14 · arxiv updated 2013/08/15

Abstract

For any compact Riemannian manifold (M,g) and its heat kernel embedding map psi_t from M into l² constructed in [BBG], we study the higher derivatives of psi_t with respect to an orthonormal basis at x on M. As the heat flow time t goes to 0, it turns out the limiting angles between these derivative vectors are universal constants independent on g, x and the choice of orthonormal basis. Geometric applications to the mean curvature and the Riemannian curvature are given. Some algebraic structures of the infinite jet space of psi_t are explored.

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