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Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
Given a class of closed Riemannian manifolds with prescribed geometric
conditions, we introduce an embedding of the manifolds into 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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