A Special Class of Finsler Geometries and de Sitter Spaces
2009jbz | D.G. Pavlov, G.I. Garas'ko, M.L. Fil'chenkov  // geom2004@mail.ru, gri9z@mail.ru, fmichael@mail.ru

Extensions of General Relativity (GR) have been considered. Reasons for generalizing GR related to difficulties of the theory itself as well as a necessity of interpreting the new astronomical observations are indicated. Numerous attempts of generalizing GR being beyond the scope of Riemannian geometry are listed.
A class of spaces conformally coupled to flat Finsler spaces is shown to be singled out among all Finsler spaces. Its dilatation-contraction coefficient and the world function, in terms of which it is expressed, depend only on an interval of the initial flat space. Then from the Finsler geometry self-sufficiency principle it follows that the dilatation-contraction coefficient is a constant divided by the interval, and the world function is a product of a constant and a logarithm of the dilatation-contraction coefficient. Each element of the class possesses an isometric symmetry group, which includes that of the initial flat Finsler space as a proper subgroup, and possesses a conformal symmetry group coinciding with that of initial flat space. If one takes Minkowski space as an initial one, then the above class space is a pseudo-Riemannian space in the four-dimensional region, where the interval in some approximation is changeable by a temporal coordinate, coinciding with de Sitter space in the same approximation.

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