On the obstruction to integrability of almost-complex structures

2008/04/04 by Valeriy Yumaguzhin, Valeriy A. Yumaguzhin, Yumaguzhin, Valeriy A.
Mathematics · Physics and Astronomy · #53A55 #53C10 #53C15 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP #msc:53A55 #msc:53C10 #msc:53C15

paper · pdf · doi:10.48550/arxiv.0804.0690

11 pages

arxiv created 2008/04/04 · openalex publication_date 2008/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The natural bundle π:E→ M of almost-complex structures is considered. The action of the pseudogroup of all diffeomorphisms of M on the total space E is investigated. A nontrivial 1-st order differential invariant of this action is constructed. It is proved that the Nijenhuise tensor of an almost-complex structures is equal to zero iff the constructed invariant for this structure is zero.

Related

• Real analytic curves of almost complex structures
• Invariants and submanifolds in almost complex geometry
• Integrability of almost complex structures on Banach manifolds
• Curvature and integrability of almost complex structures
• A Function obstruction to the Existence of Complex Structures