Foliated Manifolds and Conformal Heat Morphisms.

摘要

The objects under study, in this article, are Riemannian manifolds foliated by hypersurfaces. Looking at the transverse direction as time, the authors construct the generalized heat operator and, in the spirit of a time-space extension of harmonic morphisms, the authors introduce the conformal heat morphisms. Concrete examples of these concepts are presented, as well as, a characterization of conformal heat morphisms. Lastly, the authors calculate the heat Lie algebra of the generalized heat operator.