This article is cited in 1 paper

Holomorphic Distributions and Connectivity by Integral Curves of Distributions

Vladimir A. Zorich

Division of Mathematical Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia

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 Carathéodory in relation to classical thermodynamics, also admits a holomorphic formulation.

Keywords: holomorphic distribution, integral curve, connectivity, thermodynamic states, adiabatic transitions, Carathéodory's theorem.

MSC: 53D10, 32B15, 80A05

Received: July 19, 2019; in final form September 14, 2019; Published online September 19, 2019

Language: English

DOI: 10.3842/SIGMA.2019.070

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ArXiv: 1907.05610