Real analytic curves of almost complex structures

2024/04/15 by Sillari, Lorenzo
#32G07 (Secondary) #32Q60 (Primary) 53C15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.10079

Abstract

We prove that, on a compact almost complex manifold, the space of almost complex structures whose Nijenhuis tensor has rank at least k at every point is either empty or dense in each path-connected component of the space of almost complex structures. In particular, this applies to maximally non-integrable almost complex structures.

Related

• On the space of almost complex structures
• On the obstruction to integrability of almost-complex structures
• Almost complex manifolds with small Nijenhuis tensor
• Rank of the Nijenhuis tensor on parallelizable almost complex manifolds
• A Function obstruction to the Existence of Complex Structures