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Automorphisms of geometric structures as symmetries of differential equations. (English. Russian original) Zbl 0845.53043

Russ. Math. 38, No. 2, 1-8 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 2 (381), 3-10 (1994).
Projective and affine Lie algebras of Lorentz manifolds are investigated by using the skew-normal frame technique. The method is based on considering the algebraic structure of the Lie derivative \(L_X g\) of a metric \(g\) in the direction of a projective motion \(X\). The basis elements and the structure constants of projective Lie algebras of Lorentz manifolds are written out explicitly. From these the generators of adjoint representations are constructed. The corresponding results are used for construction of models of gauge fields. The models are developed on fibre bundles with projective or affine groups as structure groups and with \(h\)-spaces as base manifolds. The results obtained in this work open ample opportunities for investigation of symmetries of the geodesic equations in physics and mechanics.
Reviewer: G.Zet (Iaşi)

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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