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].

Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics
Caner Koca and Mehdi Lejmi "Hermitian metrics of constant Chern scalar curvature on ruled surfaces," Kodai Mathematical Journal 43(3), 409-430, (October 2020). https://doi.org/10.2996/kmj/1605063622
Published: October 2020
JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.43 • No. 3 • October 2020
Back to Top