Holomorphic Distributions and Connectivity by Integral Curves of Distributions

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dc.contributor.authorZorich, V.A.
dc.date.accessioned2025-12-04T13:02:26Z
dc.date.issued2019
dc.description.abstractIt 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.
dc.description.sponsorshipI am very grateful to S.Yu. Nemirovski for fruitful discussions and for the reference [2], where the authors not only report their impressive results, but also provide full proofs of several facts of mathematical folklore (e.g., holomorphic versions of the Darboux theorem), which they use, and which we also needed above. I am also indebted to F. Forstnerič for his argument used above, and for pointing out the new reference [1]. Special thanks to B. Khesin, who carefully read my source text and corrected not only my English but my math as well. Additional thanks go to the referees for valuable remarks and suggestions.
dc.identifier.citationHolomorphic Distributions and Connectivity by Integral Curves of Distributions / V.A. Zorich // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2019.070
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 53D10; 32B15; 80A05
dc.identifier.otherarXiv: 1907.05610
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210225
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleHolomorphic Distributions and Connectivity by Integral Curves of Distributions
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2019, том 15, випуск за цей рік