Foliated manifolds and conformal heat morphisms
type: Item
instance of: scholarly article
title: Foliated manifolds and conformal heat morphisms
zbMATH Open document ID: 1007.58010
DOI: 10.1023/A:1014929718946
author: Eric Loubeau
author: Torbjoern Kolsrud
published in: Annals of Global Analysis and Geometry
publication date: 2002-05-12T00:00:00Z
review text: Let \(M\) be a Riemannian manifold foliated by hypersurfaces. The generalized heat operator is constructed on \(M\) by looking at the transverse direction as time. The notion of harmonic morphism [\textit{B. Fuglede}, Ann. Inst. Fourier 28, No. 2, 107-144 (1978; Zbl 0339.53026) and \textit{T. Ishihara}, J. Math. Kyoto Univ. 19, 215-229 (1979; Zbl 0421.31006)] is generalized here by defining the couples consisting of a function and a map, called conformal heat morphism, which conformally pull back (local) solutions of a generalized heat operator on \(M\). A characterization and some examples are given. Then the heat Lie algebra of the generalized heat operator is calculated.
reviewed by: Cornelia-Livia Bejan
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 1738877
zbMATH Keywords: foliated manifold
zbMATH Keywords: harmonic morphism
zbMATH Keywords: conformal heat morphism
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1738877