English

An Obata-type characterization of Calabi metrics on line bundles

Differential Geometry 2020-02-21 v1 Spectral Theory

Abstract

We characterize those complete K{\"a}hler manifolds supporting a nonconstant real-valued function with critical points whose Hessian is complex linear, has pointwise two eigenvalues and whose gradient is a Hessian-eigenvector.

Keywords

Cite

@article{arxiv.2002.08810,
  title  = {An Obata-type characterization of Calabi metrics on line bundles},
  author = {Nicolas Ginoux and Georges Habib and Mihaela Pilca and Uwe Semmelmann},
  journal= {arXiv preprint arXiv:2002.08810},
  year   = {2020}
}