This article is cited in 4 papers

The full decision of Young–Mills equations for the central-symmetric metrics

Leonid N. Krivonosov^a, Vyacheslav A. Luk'yanov<sup>b

a</sup> Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
^b Zavolzhsk Branch of Nizhny Novgorod State Technical University, Zavolzhsk, Nizhegorodskaya obl., Russia

Abstract: This article develops the researches begun in [1]. The system of the differential Young–Mills equations for the central-symmetric metrics is deduced. The general solution of this system expressed through elliptic $\wp$-function of Weierstrass is resulted. For several special cases the solutions expressed through elementary functions are received. Criteria that the metrics which is the direct sum of two binary quadratic forms is Einstein metrics and the conformally-flat metrics are proved.

Keywords: curvature of the connection, Hodge operator, Einstein equations, Maxwell's equations, Young–Mills equations, central-symmetric metrics, 4-dimensional conformally connected manifold.

UDC: 514.76

Received: 11.10.2010
Received in revised form: 22.02.2011
Accepted: 10.04.2011