Mathematics
Document Type
Article
Abstract
In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical '1-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality. The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma. © 2020 Robert Ream, published by De Gruyter 2020.
Publication Title
Complex Manifolds
Publication Date
2020
Volume
7
Issue
1
First Page
129
Last Page
140
ISSN
2300-7443
DOI
10.1515/coma-2020-0007
Keywords
almost-complex manifolds, twistor space, Weyl geometry
Repository Citation
Ream, Robert, "The Adjunction Inequality for Weyl-Harmonic Maps" (2020). Mathematics. 48.
https://commons.clarku.edu/mathematics/48
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Conditions
Ream, R. (2020). The Adjunction Inequality for Weyl-Harmonic Maps. Complex Manifolds, 7(1), 129-140. https://doi.org/10.1515/coma-2020-0007
