Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 19, No. 2, pp. 245-253 (2003)

On the homogeneous geometrical model of a Riemannian space

Adrian Sandovici

University of Groningen, The Netherlands

Abstract: In the paper we study the homogeneous geometrical model of a Riemannian space. The canonical connection is analyzed in details. On this model, the Einstein equations, the electromagnetic fields and generalized Einstein-Yang Mills equations are studied. We remark that the theory we proposed in this paper works only for the case when the space test is without charges. The Einstein equations of our model projected on the basis manifold M are perturbations of the classical Einstein equations on the basis manifold M.

Keywords: homogeneous metrical structure, metrical almost $2-\pi$ structure, d-connections compatible with a metrical almost $2-\pi$ structure, Einstein equations, electromagnetic field, generalized EYM equations.

Classification (MSC2000): 53C60

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