Isometric embeddings via heat kernel

Abstract

For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t->0, asymptotic geometry of the embedded images is discussed.

39 pages. We remove the Einstein condition in the previous version. The isometric embedding is extended to all compact Riemannian manifolds with smooth metrics. The embedding is improved to C^k regularity for any given k. Proofs are simplified, and less relevant results are removed

References in corpus (2)

• Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
• Euclidean Embeddings and Riemannian Bergman Metrics

Cited by in corpus (1)

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