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arXiv · 1911.10938

Bismut type formulae for differential forms

K. D. Elworthy·Xue-Mei Li
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Abstract

Formulae are given for $dP_t ϕ$, $d^*P_tϕ$ and $ΔP_tϕ$ for $P_t$ the heat semigroup acting on a q-form $ϕ$. The formulae are Brownian motion expectations of $ϕ$ composed with random translations determined by Weitzenbock curvarure terms. Derivatives of the curvature are not involved.

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K. D. Elworthy, Xue-Mei Li. 2019-11-21. Bismut type formulae for differential forms. https://doi.org/10.1016/s0764-4442(98)80108-0

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