## A heat flow approach to the Godbillon-Vey class.(English)Zbl 1358.58016

Summary: We give a heat flow derivation for the Godbillon Vey class. In particular we prove that if $$(M,g)$$ is a compact Riemannian manifold with a codimension 1 foliation $$\mathcal{F}$$, defined by an integrable 1-form $$\omega$$ such that $$||\omega||=1$$, then the Godbillon-Vey class can be written as $$[-\mathcal{A} \omega \wedge d\omega]_{dR}$$ for an operator $$\mathcal{A} :\Omega^*(M)\rightarrow \Omega^*(M)$$ induced by the heat flow.

### MSC:

 58J65 Diffusion processes and stochastic analysis on manifolds 53C12 Foliations (differential geometric aspects) 60H30 Applications of stochastic analysis (to PDEs, etc.) 60J60 Diffusion processes
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