Foliated manifolds and conformal heat morphisms (Q1597182)

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.