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A smooth gauge model on tangent bundle. (English) Zbl 1178.53026

Summary: The tangent manifold \(T M\) of a smooth, paracompact manifold \(M\), fibered over \(M\) by the natural projection \(\pi\), carries an integrable distribution ker\(\pi_\ast\), called vertical distribution. If one takes a supplementary distribution of it, called horizontal, an almost complex structure \(F_S\) appears. One endowes the vertical distribution with a Riemmanian metric \(\gamma\). Then \(\gamma\) can be prolonged to a Riemannian metric \(G_S\) on \(T M\) such that the pair \((F_S, G_S)\) becomes an almost Hermitian structure.
In this paper some deformations of \(F_S\) and \(G_S\) are proposed and new almost Hermitian structures are determined. With respect to some gauge objects, some properties of these structures are pointed out. For a smooth gauge geometrical model determined by one of these almost Hermitian structures, the general form of the corresponding Einstein-Yang Mills equations is obtained.

MSC:

53B35 Local differential geometry of Hermitian and Kählerian structures
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C80 Applications of global differential geometry to the sciences
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