A structure theorem of Dirac-harmonic maps between spheres

Details A structure theorem of Dirac-harmonic maps between spheres A structure theorem of Dirac-harmonic maps between spheres

2008-06-24

arxiv.org/abs/0806.3803v1

Mathematics

Differential Geometry

12 pages

Scientific paper

For an arbitrary Dirac-harmonic map $(\phi,\psi)$ between compact oriented
Riemannian surfaces, we shall study the zeros of $|\psi|$. With the aid of
Bochner-type formulas, we explore the relationship between the order of the
zeros of $|\psi|$ and the genus of $M$ and $N$. On the basis, we could clarify
all of nontrivial Dirac-harmonic maps from $S^2$ to $S^2$.

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