Abstract
The behavior of harmonic maps from a domain in R 4 into S 3 is discussed. In this paper, we show that if u is a strictly stable stationary harmonic map : B 4→ S 3 , such that the singular set Sing( u) of u consists of {0}, then the degree deg( u,0) of u at 0 is zero; and that if u is a weakly stable harmonic map B 4→ S 3 with Sing( u)={0}, then deg( u,0)=0 or ±1. Furthermore, the characterization of homogeneous stable stationary harmonic maps from B 4 into S 3 is given.
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