Dirac-geodesics and their heat flows

Qun Chen, Jürgen Jost, Linlin Sun, and Miaomiao Zhu

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Submission date: 29. Apr. 2015
Pages: 20
published in: Calculus of variations and partial differential equations, 54 (2015) 3, p. 2615-2635 
DOI number (of the published article): 10.1007/s00526-015-0877-3
Bibtex
MSC-Numbers: 58E10, 58J35, 53C22, 53C27
Keywords and phrases: Dirac-geodesics, heat flow
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Abstract:
Dirac-geodesics are Dirac-harmonic maps from one dimensional domains. In this paper, we introduce the heat flow for Dirac-geodesics and establish its long-time existence and an asymptotic property of the global solution. We classify Dirac-geodesics on the standard 2-sphere S²(1) and the hyperbolic plane ℍ², and derive existence results on topological spheres and hyperbolic surfaces. These solutions constitute new examples of coupled Dirac-harmonic maps (in the sense that the map part is not simply a harmonic map).