Work

On canonical metrics of complex surfaces with split tangent and related geometric PDEs

Year: 2025

Type: article

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} .

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0021

Authors: Hao Fang, Joshua Jordan

Institution: University of Iowa

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: RTG: Geometry and Topology at Iowa