Non-existence of Higgs fields on Calabi-Yau Manifolds

Abstract

In this article, we study the Higgs vector bundles $(E,\theta )$ over a compact Calabi-Yau manifolds $X$. We use Yang-Mills-Higgs flow to prove that if a semistable Higgs bundle with vanishing Chern classes over a compact connected Calabi-Yau manifold, then the Higgs field $\theta$ is trivial. In particular, the vector bundle $E$ must be semistable.

the main results had been obtained in other authors' paper

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Cited by in corpus (1)

• The behavior of sequences of solutions to the Hitchin-Simpson equations