English

Holomorphic Distributions and Connectivity by Integral Curves of Distributions

Complex Variables 2019-09-20 v2

Abstract

It is known that the classical Frobenius theorem on conditions of integrability for distributions of planes can be extended to the case of complex holomorphic distributions. We show that an alternative criterion for integrability, namely, non-connectivity, discovered (or at least, marked and explicitly formulated) by Carath\'eodory in relation to classical thermodynamics, also admits a holomorphic formulation.

Keywords

Cite

@article{arxiv.1907.05610,
  title  = {Holomorphic Distributions and Connectivity by Integral Curves of Distributions},
  author = {Vladimir A. Zorich},
  journal= {arXiv preprint arXiv:1907.05610},
  year   = {2019}
}