This article is cited 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

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.

UDC: 515.1+519.3+513.7

Received: 26.11.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:3, 56–60

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