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}
}