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
Mots-clés : conform connection, quadric signature
@article{IVM_2009_3_a3,
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/}
}
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/