The Heat Equation for Riemannian Foliations

DOI10.2307/2001257zbMath0702.58074OpenAlexW4234754266MaRDI QIDQ3480970

Philippe Tondeur, Seiki Nishikawa, Mohan Ramachandran

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001257

zbMATH Keywords

existenceheat equationuniquenessRiemannian foliationLaplacianHodge-de Rham type decomposition

Mathematics Subject Classification ID

Heat equation (35K05) Hodge theory in global analysis (58A14) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

Deforming metrics of foliations ⋮ Heat conduction for Riemannian foliations ⋮ Harmonic maps of foliated Riemannian manifolds ⋮ Hodge decomposition along the leaves of Riemannian foliation ⋮ Smoothness of isotopy for symplectic pairs ⋮ Traces of heat operators on Riemannian foliations ⋮ De Rham-Hodge-Kodaira decomposition in \(\infty\)-dimensions ⋮ Hilbert complexes ⋮ A finiteness theorem for transitive foliations and flat vector bundles

Cites Work

• Décomposition de Hodge basique pour les feuilletages riemanniens
• De Rham-Hodge theory for Riemannian foliations
• Foliations on Riemannian manifolds
• Comparing Riemannian foliations with transversally symmetric foliations
• An asymptotic expansion for the heat equation
• Harmonic Forms and Heat Conduction
• An ergodic theorem associated with harmonic integrals
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