A moment map for twisted-Hamiltonian vector fields on locally conformally K\"ahler manifolds

TL;DR

This paper generalizes the concept of scalar curvature as a moment map from K"ahler geometry to the broader setting of locally conformally K"ahler manifolds, expanding the theoretical framework.

Contribution

It introduces a moment map framework for twisted-Hamiltonian vector fields on locally conformally K"ahler manifolds, extending classical geometric interpretations.

Findings

Scalar curvature interpreted as a moment map in the new setting

Extension of Donaldson-Fujiki interpretation to locally conformally K"ahler geometry

Broader understanding of geometric structures on complex manifolds

Abstract

We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in K\"ahler Geometry to the wider framework of locally conformally K\"ahler Geometry.