Journal article
On canonical metrics of complex surfaces with split tangent and related geometric PDEs
Journal für die reine und angewandte Mathematik, Vol.2025(823), pp.255-289
2025
DOI: 10.1515/crelle-2025-0021
Abstract
In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent and construct 2 types of metric cones, which are natural analogues of the Kähler case. We introduce a new type of fully nonlinear geometric PDE on such surfaces and establish smooth solvability. As a geometric application, we solve the prescribed Bismut–Ricci problem. We also introduce a weighted version of this problem. With this, we obtain canonical metrics on two important classes of complex surfaces: primary Hopf surfaces and Inoue surfaces of type S M \mathcal{S}_{M} .
Details
- Title: Subtitle
- On canonical metrics of complex surfaces with split tangent and related geometric PDEs
- Creators
- Hao Fang - University of IowaJoshua Jordan - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal für die reine und angewandte Mathematik, Vol.2025(823), pp.255-289
- DOI
- 10.1515/crelle-2025-0021
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- Publisher
- WALTER DE GRUYTER GMBH
- Grant note
- National Science Foundation
Both authors would like to thank Connor Mooney, Jeff Streets, Lihe Wang and Jinyang Wu for discussions. They appreciate valuable comments of Jeff Streets on an earlier draft of this paper. The first named author thanks Bo Guan, Biao Ma, Wei Wei and Fangyang Zheng for discussions.
- Language
- English
- Electronic publication date
- 03/28/2025
- Date published
- 2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984805013002771
Metrics
7 Record Views