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Long Time Behaviour of Leafwise Heat Flow for Riemannian Foliations

Published online by Cambridge University Press:  04 December 2007

Jesús A. Álvarez López  and
Yuri A. Kordyukov
Jesús A. Álvarez López
Affiliation:
Departamento de Xeometría e Topoloxía, Facultade de Matemáticas Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain. E-mail: alvarez@zmat.usc.es
Yuri A. Kordyukov
Affiliation:
Department of Mathematics, Ufa State Aviation Technical University, 12 K. Marx str., 450025 Ufa, Russia. E-mail: yurikor@math.ugatu.ac.ru
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Abstract

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For any Riemannian foliation $\cal F$ 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 $\cal F$.

Keywords

foliationbundle-like metricleafwise heat flowdifferential formspectral sequence
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 2 , January 2001 , pp. 129 - 153
Copyright
© 2001 Kluwer Academic Publishers