#### Heat Equation Derivative Formulas
for Vector Bundles

by Bruce K. Driver and Anton Thalmaier

We use martingale methods to give Bismut type derivative formulas
for differentials and co-differentials of heat semigroups on forms, and more
generally for sections of vector bundles. The formulas are mainly in terms
of Weitzenböck curvature terms, in most cases derivatives of the
curvature are not involved. In particular, our results improve the formula
in Driver (1997) for logarithmic derivatives of the heat kernel
measure on a Riemannian manifold. Our formulas also include the formulas in
Elworthy and Li (1999).
*Journal of Functional Analysis * **183** (2001) 42-108

The paper is available here:

Bruce K. Driver
<driver@euclid.ucsd.edu>
Anton Thalmaier
<anton.thalmaier@uni.lu>
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