Dirac-harmonic maps between Riemann surfaces
Qun Chen, Jürgen Jost, Linlin Sun, and Miaomiao Zhu
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Submission date: 10. Nov. 2015
published in: The Asian journal of mathematics, 23 (2019) 1, p. 107-125
DOI number (of the published article): 10.4310/AJM.2019.v23.n1.a6
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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.