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An Obata-type characterization of Calabi metrics on line bundles

Published 20 Feb 2020 in math.DG and math.SP | (2002.08810v1)

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.

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