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October 2020 Hermitian metrics of constant Chern scalar curvature on ruled surfaces
Caner Koca, Mehdi Lejmi
Kodai Math. J. 43(3): 409-430 (October 2020). DOI: 10.2996/kmj/1605063622

Abstract

It is known that Hirzebruch surfaces of non zero degree do not admit any constant scalar curvature Kähler metric [6, 22, 38]. In this note, we describe how to construct Hermitian metrics of positive constant Chern scalar curvature on Hirzebruch surfaces using Page-Bérard-Bergery's ansatz [41, 14]. We also construct the interesting case of Hermitian metrics of zero Chern scalar curvature on some ruled surfaces. Furthermore, we discuss the problem of the existence in a conformal class of critical metrics of the total Chern scalar curvature, studied by Gauduchon in [26, 27].

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Caner Koca. Mehdi Lejmi. "Hermitian metrics of constant Chern scalar curvature on ruled surfaces." Kodai Math. J. 43 (3) 409 - 430, October 2020. https://doi.org/10.2996/kmj/1605063622

Information

Published: October 2020
First available in Project Euclid: 11 November 2020

MathSciNet: MR4173158
Digital Object Identifier: 10.2996/kmj/1605063622

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 3 • October 2020
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