Long Time Behaviour of Leafwise Heat Flow for Riemannian Foliations |
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| Authors: | Jesús A Álvarez López Yuri A Kordyukov |
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| Institution: | (1) Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain;(2) Department of Mathematics, Ufa State Aviation Technical University, 12 K. Marx str., 450025 Ufa, Russia |
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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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| Keywords: | foliation bundle-like metric leafwise heat flow differential form spectral sequence |
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