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Название статьи AFFINOR METRIC STRUCTURES AND THEIR PHYSICAL APPLICATIONS
Авторы

Kornev E., Kemerovo State University, Krasnaya Str. 6, Kemerovo, 650043 Russian Federation, q148@mail.ru

Раздел: MATHEMATICAL  SCIENCES
Год 2016 Номер журнала 2 DOI 10.21603/2500-1418-2016-1-2-34-40
Аннотация This work describes the fundamentals of the mathematical theory of affinor metric structures and physical problems where these structures are used. Affinor metric structure is defined as an arbitrary 1-form having a radical of arbitrary rank, a certain Riemannian metric and a special field of automorphisms of tangent spaces connecting the exterior differential of this 1-form and a metric. Affinor metric structures are a generalization of almost contact metric structures and Kahlerian structures with a precise fundamental 2-form. At the end of the work, applications of affinor metric structures in physics are described. The purpose of this article is to demonstrate possibilities of application of the theory of affinor metric structures when solving various mathematical and physical problems. In particular, the use of such structures to search for closed curves with a nonzero circulation of a vector field and construction of submanifolds on which the exterior differential of some 1-form induced by a vector field is non-degenerated. Methods of Riemann geometry and theories of differential forms and mathematical analysis on manifolds were used. The relevance of the subject matter is due to the most common case of statement of the problem for some 1-form with radical of arbitrary dimension. While in classic case, physics and geometry consider only 1-forms with a zero radical.
Ключевые слова Affinor metric structure, radical of a 1-form, vector field effect on a curve
Информация о статье Дата поступления 17 мая 2016 года
Дата принятия в печать 28 июля 2016 года
Дата онлайн-размещения 30 декабря 2016 года
Выходные данные статьи Kornev E. AFFINOR METRIC STRUCTURES AND THEIR PHYSICAL APPLICATIONS. Science Evolution, 2016, vol. 1, no. 2, pp. 34-40. doi:10.21603/2500–1418–2016–1–2–34–40.
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Список цитируемой литературы
  • Calvaruso G. Three-dimensional homogeneous almost contact metric structures. Journal of Geometry and Physics, 2013, vol. 69, pp. 60-73.
  • Kornev E.S. Invariantnye affinornye metricheskie struktury na gruppakh Li [Invariant affinor metric structures on Lie groups]. Sibirskiy matematicheskiy zhurnal [Siberian Mathematical Journal], 2012, vol. 53, no. 1, pp. 107-123.
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  • Kornev E.S., Slavolyubova Ya.V. Invariantnye affinornye i subkelerovy struktury na odnorodnykh prostranstvakh [Invariant affinor and sub-Kahlerian structures on homogeneous spaces]. Sibirskiy matematicheskiy zhurnal [Siberian Mathematical Journal], 2016, vol. 57, no. 1, pp. 51-63.
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Copyright © 2016, KemSU. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), allowing third parties to copy and redistribute the material in any medium or format and to remix, transform, and build upon the material for any purpose, even commercially, provided the original work is properly cited and statesitslicense. This article is published with open access at http://science-evolution.ru.

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Последний выпуск: Science Evolution, Vol. 2, no. 1, 2017