Almost Complex Structure on S²ⁿ

2011/04/04 by Jianwei Zhou, Zhou, Jianwei
Mathematics · #53B35 #53C05 #57R20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B35 #msc:53C05 #msc:57R20

paper · pdf · doi:10.48550/arxiv.1104.0505

4 pages

arxiv created 2011/04/04 · arxiv updated 2011/04/05

Abstract

We show that there is no complex structure in a neighborhood of the space of orthogonal almost complex structures on the sphere S²ⁿ, n>1. The method is to study the first Chern class of vetcor bundle T^(1,0)S²ⁿ.

Related

• The Complex Structures on S²ⁿ
• S.-S. Chern's study of almost-complex structures on the six-sphere
• Almost Complex Structures on Homotopy Complex Projective Spaces
• Almost Complex Structures on (n-1)-connected 2n-manifolds
• On the space of almost complex structures