Asian Journal of Mathematics

Volume 23 (2019)

Number 1

Dirac-harmonic maps between Riemann surfaces

Pages: 107 – 126

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n1.a6

Authors

Qun Chen (School of Mathematics and Statistics, Wu Han University, Hubei, China)

Jürgen Jost (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Linlin Sun (School of Mathematics and Statistics, Wu Han University, Hubei, China)

Miaomiao Zhu (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Abstract

In this paper, we consider the existence and structure of Dirac-harmonic maps between closed Riemann surfaces. Utilizing the Riemann–Roch formula, we compute the dimension of harmonic spinors along a map, based on which we prove an existence theorem for Dirac-harmonic maps between closed Riemann surfaces. We also obtain a structure theorem for Dirac-harmonic maps between two surfaces if their genera and the degree of the map satisfy a certain relation.

Keywords

Dirac-harmonic maps, Riemann surfaces, Riemann–Roch formula

2010 Mathematics Subject Classification

53C27, 53C43

Full Text (PDF format)

Qun Chen is partially supported by NSFC of China.

Linlin Sun is partially supported by CSC of China.

Miaomiao Zhu is supported in part by NSFC of China (No. 11601325).

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programe (FP7/2007-2013) / ERC grant agreement no. 267087.

Received 31 March 2016

Accepted 27 July 2017

Published 3 May 2019