Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres

2013/01/29 by Yunhee Euh, Euh, Yunhee, Kouei Sekigawa +1
Mathematics · #53C15 #53C21 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C15 #msc:53C21 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1301.6835

openalex publication_date 2013/01/29 · arxiv created 2013/01/30 · arxiv updated 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.

Related

• Curvature, integrability, and the six sphere
• Non-existence of orthogonal complex structures on 6-sphere with a metric close to the round one
• Curvature and integrability of almost complex structures
• (a, 1)f structures on product of spheres
• Induced structures on product of spheres