Holomorphic Distributions and Connectivity by Integral Curves of Distributions

Symmetry Integrability and Geometry-Methods and Applications

article

Vladimir A. Zorich¹ 

[1] Division of Mathematical Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

关键词: holomorphic distribution;    integral curve;    connectivity;    thermodynamic states;    adiabatic transitions;    Carath´eodory’s theorem;   

DOI  :  10.3842/SIGMA.2019.070

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown