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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 070, 6 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.070
(Mi sigma1506)
 

This article is cited in 1 scientific paper (total 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
Full-text PDF (232 kB) Citations (1)
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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.
Received: July 19, 2019; in final form September 14, 2019; Published online September 19, 2019
Bibliographic databases:
Document Type: Article
MSC: 53D10, 32B15, 80A05
Language: English
Citation: Vladimir A. Zorich, “Holomorphic Distributions and Connectivity by Integral Curves of Distributions”, SIGMA, 15 (2019), 070, 6 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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