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Long time behavior of leafwise heat flow for Riemannian foliations

Jesus A. Alvarez Lopez·Yuri A. Kordyukov
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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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Jesus A. Alvarez Lopez, Yuri A. Kordyukov. 2025-05-14. Long time behavior of leafwise heat flow for Riemannian foliations. https://arxiv.org/abs/dg-ga/9612010

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