On the obstruction to integrability of almost-complex structures

Valeriy A. Yumaguzhin

On the obstruction to integrability of almost-complex structures

Differential Geometry 2008-04-07 v1 Mathematical Physics math.MP

Authors: Valeriy A. Yumaguzhin

Abstract

The natural bundle $\pi:E\to M$ 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.

Keywords

vector bundles

Cite

@article{arxiv.0804.0690,
  title  = {On the obstruction to integrability of almost-complex structures},
  author = {Valeriy A. Yumaguzhin},
  journal= {arXiv preprint arXiv:0804.0690},
  year   = {2008}
}

Comments

11 pages

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