Geodesic
Yang--Mills equations in 4-dimensional conform connection manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2009), pp. 67-72.

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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, curvature of the connection, Hodge operator, real quadrics, Yang-Mills functional.
Mots-clés : conform connection, quadric signature 
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     author = {V. A. Luk'yanov},
     title = {Yang--Mills equations in 4-dimensional conform connection manifolds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--72},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_3_a3/}
}
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V. A. Luk'yanov. Yang--Mills equations in 4-dimensional conform connection manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2009), pp. 67-72. http://geodesic.mathdoc.fr/item/IVM_2009_3_a3/

[1] Besse A., Mnogoobraziya Einshteina, T. 1, Mir, M., 1990, 318 pp. | MR | Zbl