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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 3, Pages 67–72 (Mi ivm1268)  

This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

Yang–Mills equations in 4-dimensional conform connection manifolds

V. A. Luk'yanov

Zavolzhsk Branch of Nizhny Novgorod State Technical University
Full-text PDF (162 kB) Citations (5)
References:
Abstract: In this article on the simplest examples of compact 4-dimensional conform connection manifolds (real quadrics in 5-dimensional projective space) we show that the only invariant, quadratic relatively to the curvature $\Phi$ of the connection, is Yang–Mills functional $\int\vert\operatorname{tr}(\ast\Phi\wedge\Phi)\vert$. The author of the article doesn't know, whether 4-form $\vert\operatorname{tr}(\ast\Phi\wedge\Phi)\vert$ is invariant in any 4-dimensional conform connection manifold.
Keywords: Bianchi identity, compact 4-dimensional manifold, conform connection, curvature of the connection, Hodge operator, quadric signature, real quadrics, Yang-Mills functional.
Received: 26.11.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 3, Pages 56–60
DOI: https://doi.org/10.3103/S1066369X09030049
Bibliographic databases:
Document Type: Article
UDC: 515.1+519.3+513.7
Language: Russian
Citation: V. A. Luk'yanov, “Yang–Mills equations in 4-dimensional conform connection manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 3, 67–72; Russian Math. (Iz. VUZ), 53:3 (2009), 56–60
Citation in format AMSBIB
\Bibitem{Luk09}
\by V.~A.~Luk'yanov
\paper Yang--Mills equations in 4-dimensional conform connection manifolds
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 3
\pages 67--72
\mathnet{http://mi.mathnet.ru/ivm1268}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2581454}
\zmath{https://zbmath.org/?q=an:1188.58006}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 3
\pages 56--60
\crossref{https://doi.org/10.3103/S1066369X09030049}
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  • https://www.mathnet.ru/eng/ivm/y2009/i3/p67
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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