Holomorphic Distributions and Connectivity by Integral Curves of Distributions
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 explici...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210225 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Holomorphic 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862612390387908608 |
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| author | Zorich, V.A. |
| author_facet | Zorich, V.A. |
| citation_txt | Holomorphic 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T21:24:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210225 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:48Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zorich, V.A. 2025-12-04T13:02:26Z 2019 Holomorphic 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. 1815-0659 2010 Mathematics Subject Classification: 53D10; 32B15; 80A05 arXiv: 1907.05610 https://nasplib.isofts.kiev.ua/handle/123456789/210225 https://doi.org/10.3842/SIGMA.2019.070 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. I 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Holomorphic Distributions and Connectivity by Integral Curves of Distributions Article published earlier |
| spellingShingle | Holomorphic Distributions and Connectivity by Integral Curves of Distributions Zorich, V.A. |
| title | Holomorphic Distributions and Connectivity by Integral Curves of Distributions |
| title_full | Holomorphic Distributions and Connectivity by Integral Curves of Distributions |
| title_fullStr | Holomorphic Distributions and Connectivity by Integral Curves of Distributions |
| title_full_unstemmed | Holomorphic Distributions and Connectivity by Integral Curves of Distributions |
| title_short | Holomorphic Distributions and Connectivity by Integral Curves of Distributions |
| title_sort | holomorphic distributions and connectivity by integral curves of distributions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210225 |
| work_keys_str_mv | AT zorichva holomorphicdistributionsandconnectivitybyintegralcurvesofdistributions |