Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space

Abstract

We introduce generalized Kazdan-Warner equations on Riemannian manifolds associated with a linear action of a torus on a complex vector space. We show the existence and the uniqueness of the solution of the equation on any compact Riemannian manifold. As an application, we give a new proof of a theorem of Baraglia which asserts that a cyclic Higgs bundle gives a solution of the periodic Toda equation.

The numbering of theorems, propositions, examples, corollaries, lemmas, definitions, and remarks has been made the same as in the published version. 23 pages

Cited by in corpus (2)

• The geometric Toda equations for noncompact symmetric spaces
• On diagonal pluriharmonic metrics of $G$-Higgs bundles