Are different geometries really that different?

Details Are different geometries really that different? Are different geometries really that different?

2009-06-16

arxiv.org/abs/0906.2921v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 2 figures, talk that will be presented at PIRT-2009, July (Russia), one misprint is removed, formulation of the theo

Scientific paper

Here is presented a concept of centrogeometry which can be seen as a combination of the concept of point-like observer with an idea of Poincar\'{e}'s that different geometries are principally equivalent. As it is to be shown later, all centrogeometries are obtained from each other by general deformation (i.e. active coordinate transformations). Isometries of centrogeometries are equivalent to those of the Euclidean centrogeometry as described by common diffeomorphisms of the Euclidean spheres. There are discussed physical aspects of centrogeometry in the context of chronogeometry, mechanics and cosmology.

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