On pseudo-harmonic maps in conformal geometry

TL;DR

This paper extends harmonic map techniques to conformal geometry, proving new rigidity results and topological obstructions for Kahler-Weyl manifolds, including applications to Vaisman's conjecture.

Contribution

It generalizes harmonic map methods to Kahler-Weyl geometry, extending Siu's rigidity and establishing topological constraints on Kahler-Weyl structures.

Findings

Extended Siu's rigidity to Kahler-Weyl geometry

Proved topological obstructions for certain Kahler-Weyl manifolds

Showed no co-compact lattice in SO(1,n) can be fundamental group of some Kahler-Weyl manifolds

Abstract

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications include topological obstructions to the existence of Kahler-Weyl structures. For example, we show that no co-compact lattice in SO(1,n), n>2, can be the fundamental group of a compact Kahler-Weyl manifold of certain type.