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arXiv · 2002.09141

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

Natsuo Miyatake
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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.

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Natsuo Miyatake. 2020-02-21. Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space. https://doi.org/10.1007/s10711-021-00632-z

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