Embedding Riemannian manifolds by the heat kernel of the connection Laplacian

作者：Wu Hau Tieng^*

来源：Advances in Mathematics, 2017, 304: 1055-1079.

DOI：10.1016/j.aim.2016.05.023

• Vector diffusion map
• Spectral geometry
• Precompactness
• Graph connection Laplacian
• Spectral graph theory

Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into l(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.

• 出版日期2017-1-2