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We show that any closed $n$-dimensional manifold $(M,g)$ can be embedded by amap constructed using the heat kernels of the connection Laplacian as well as amaps constructed using truncated heat kernel at a certain time $t$ from a$\delta$-net $\{q_i\}_{i=1}^{N_0}$ via a rescaling trick. Both the time $t$ and$N_0$ are bounded in terms of the dimension, bounds on the Ricci curvature andits derivative, the injectivity radius, and the volume. Moreover, both maps canbe made arbitrarily close to an isometry.

Manifold embeddings by heat kernels of connection Laplacian