Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian

Hau-tieng Wu

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arXiv · 1305.4232

Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian

Hau-tieng Wu

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Abstract

Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle. As a result, we can construct a distance in this class which leads to a pre-compactness theorem on the class under consideration.

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Hau-tieng Wu. 2013-05-18. Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian. https://arxiv.org/abs/1305.4232

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