A structure theorem of Dirac-harmonic maps between spheres
- 300 Downloads
For an arbitrary Dirac-harmonic map (φ,ψ) between compact oriented Riemannian surfaces, we shall study the zeros of |ψ|. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of |ψ| and the genus of M and N. On the basis, we could clarify all of non-trivial Dirac-harmonic maps from S 2 to S 2.
Mathematics Subject Classification (2000)58E20 53C27
The author wishes to express his sincere gratitude to Professor Y.L. Xin in Fudan University, for his inspiring suggestions.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.
- 4.Friedrich, T.: Dirac operators in Riemannian geometry. Graduate Studies in Mathematics, vol. 25. American Mathematical Society, Providence, pp. xvi+195 (2000)Google Scholar
- 5.Hijazi, O.: Spectral properties of the Dirac operator and geometrical structures. In: Proceedings of the Summer School on Geometric Methods in Quantum Field Theory. 12–30 July 1999, Villa de Leyva, Colombia, World Scientific, Physics (2001)Google Scholar
- 7.Schoen, R., Yau, S.T.: Lectures on harmonic maps. Conference Proceedings and Lecture Notes in Geometry and Topology, II. International Press, Cambridge (1997)Google Scholar
- 10.Zhu, M.: Dirac-harmonic maps from degenerating spin surfaces I: the Neveu–Schwarz case. arxiv: 0803. 3723.Google Scholar
Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.