Asian Journal of Mathematics
Volume 23 (2019)
Dirac-harmonic maps between Riemann surfaces
Pages: 107 – 126
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.
Dirac-harmonic maps, Riemann surfaces, Riemann–Roch formula
2010 Mathematics Subject Classification
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