  For any compact Riemannian manifold $(M,g)$ and its heat kernel embedding map
$psi_t$ from M into $l^2$ constructed in [BBG], we study the higher derivatives
of $psi_t$ with respect to an orthonormal basis at $x$ on $M$. As the heat flow
time $t$ goes to 0, it turns out the limiting angles between these derivative
vectors are universal constants independent on $g$, $x$ and the choice of
orthonormal basis. Geometric applications to the mean curvature and the
Riemannian curvature are given. Some algebraic structures of the infinite jet
space of $psi_t$ are explored.

Differential Geometry;Spectral Theory