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

Hao Fang; Joshua Jordan

doi:10.48550/arxiv.2406.14007

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

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

Hao Fang and Joshua Jordan

arXiv.org

Cornell University

06/20/2024

DOI: 10.48550/arxiv.2406.14007

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent bundle and construct 2 types of metric cones. We introduce a new type of fully non-linear geometric PDE on such surfaces and establish smooth solutions. As a geometric application, we solve the prescribed Bismut Ricci problem. In various settings, we obtain canonical metrics on 2 important classes of complex surfaces: primary Hopf surfaces and Inoue surfaces of type $\mathcal{S}_{M}$.

Mathematics - Differential Geometry

Details

Title: Subtitle: On canonical metrics of complex surfaces with split tangent and related geometric PDEs
Creators: Hao Fang
Joshua Jordan
Resource Type: Preprint
Publication Details: arXiv.org
DOI: 10.48550/arxiv.2406.14007
eISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 06/20/2024
Academic Unit: Mathematics
Record Identifier: 9984649043002771

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