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Dirac-harmonic maps between Riemann surfaces. (English) Zbl 1425.53056

Summary: 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.

MSC:

53C27 Spin and Spin\({}^c\) geometry
53C43 Differential geometric aspects of harmonic maps
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