English

Locally Monge-Ampere Foliations

Complex Variables 2014-03-18 v2

Abstract

It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Amp\`ere foliations and that parabolic leaves cannot have hyperbolic behavior. The result holds true also for locally Monge-Amp\`ere foliations with parabolic leaves of arbitrary codimension.

Keywords

Cite

@article{arxiv.1311.1226,
  title  = {Locally Monge-Ampere Foliations},
  author = {Morris Kalka and Giorgio Patrizio},
  journal= {arXiv preprint arXiv:1311.1226},
  year   = {2014}
}

Comments

Updated version, with correction of misprints

R2 v1 2026-06-22T02:01:51.095Z