Hopf纤维上的次椭圆调和映射

Subelliptic Harmonic Maps Based on the Hopf-Fibration

研究了由Hopf纤维诱导的次椭圆调和映射,在Hopf同伦不变量的条件下有关次椭圆调和映射存在性定理.该定理说明次椭圆调和映射有与调和映射相似的性质,而且椭圆调和映射条件显然比调和映射要弱.

On the condition of harmonic Map, we have got good conclusions. The issue people have always been concerned is whether the condition can be weakened or relaxed to enable us to get better conclusions. We study harmonic maps of the subelliptic type which is induced by Hopf - Fibration. In the content of Hopf equivariant maps, we get the existence of subelliptic harmonic maps. We show that subelliptic harmonic maps have similar properties with harmonic maps, while the subelliptic harmonic maps is a weaker condition. The results in this article will help us to get more results on existence and nonexistence of subelliptic harmonic maps.