TL;DR
This paper introduces pseudoharmonic morphisms, a new class of harmonic maps satisfying a weaker geometric condition than conformality, and explores their properties, structures, and harmonicity conditions.
Contribution
It defines the PHWC condition, characterizes pseudoharmonic morphisms, and constructs an associated canonical f-structure to analyze harmonicity.
Findings
Pseudoharmonic morphisms include harmonic morphisms.
A canonical f-structure is associated with maps satisfying (PHWC).
Conditions on the f-structure ensure the harmonicity of the maps.
Abstract
We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called {\em pseudoharmonic morphisms}, include harmonic morphisms and can be described as pulling back certain germs to certain other germs. Finally, we construct a canonical f-structure associated to every map satisfying (PHWC) and find conditions on this f-structure to ensure the harmonicity of the map.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology