The dimension and structure of the space of harmonic 2-spheres in the m-sphere

• 成果类型: Article
• 署名作者: Fernandez, Luis
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.3.3
• 发表日期: 2012
• 页码: 1093-1125
• 关键词: immersions; MAPS; SURFACES; s2

摘要

We prove the conjecture, posed in 1993 by Bolton and Woodward, that the dimension of the space of harmonic maps from the 2-sphere to the 2n-sphere is 2d + n(2). We also give an explicit algebraic method to construct all harmonic maps from the 2-sphere to the m-sphere.