Long time behavior of leafwise heat flow for Riemannian foliations

1996/12/10 by Lopez, Jesus A. Alvarez, Kordyukov, Yuri A.
#57R30 #58A14 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.dg-ga/9612010

Abstract

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about the space of bundle-like metrics on M, about the dimension of the space of leafwise harmonic forms, and mainly about the second term of the differentiable spectral sequence of F.

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