Hypercomplex Numbers, Associated Metric Spaces, and Extension of Relativistic Hyperboloid

Details Hypercomplex Numbers, Associated Metric Spaces, and Extension of Relativistic Hyperboloid Hypercomplex Numbers, Associated Metric Spaces, and Extension of Relativistic Hyperboloid

2002-06-03

arxiv.org/abs/gr-qc/0206004v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to introduce appropriate multilinear metric forms in the treatment. The scalar polyproduct, which extends the ordinary scalar product used in bilinear (Euclidean and pseudo-Euclidean) theories, has been proposed and applied to be a generalized metric base for the approach. A fundamental concept of multilinear isometry is proposed. This renders possible to muse upon various relativistic physical applications based on anisotropic {\it versus} ordinary spatially-rotational case.

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