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arXiv · 1308.0410

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

Ke Zhu
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Abstract

For any compact Riemannian manifold $(M,g)$ and its heat kernel embedding map $psi_t$ from M into $l^2$ 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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Ke Zhu. 2013-08-14. High-jet relations of the heat kernel embedding map and applications. https://arxiv.org/abs/1308.0410

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