On models of non-Eucludian spaces generated by associative algebras

Details On models of non-Eucludian spaces generated by associative algebras On models of non-Eucludian spaces generated by associative algebras

2009-12-09

arxiv.org/abs/0912.1654v1

Mathematics

Differential Geometry

11 pages, 1 figure; extended version of 0809.0946

Scientific paper

We present the non-trivial example how to generate non-Euclidean geometries from associative unital algebras. We consider bundles of the sphere of the degenerate non-Eucleadian space and its two models. The first (conformal) model is obtained by the mapping S onto a plane pass through the origin. It is analogous to the stereographic mapping. The second model (projective) is con- structed by the Norden normalization method, where we project the sphere onto a plane of normalization defining the metric and Christoffel symbols which allow us to find geodesic curves.

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