Open AccessDe Sitter Space as a Computational Tool for Surfaces and Foliations
Author(s) -
Maciej Czarnecki,
Szymon M. Walczak
Publication year - 2013
Publication title -
american journal of computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 2161-1211
pISSN - 2161-1203
DOI - 10.4236/ajcm.2013.31a001
Subject(s) - de sitter space , hyperplane , conformal map , de sitter universe , anti de sitter space , mathematics , de sitter invariant special relativity , space (punctuation) , invariant (physics) , euclidean geometry , euclidean space , computation , pure mathematics , mathematical physics , mathematical analysis , physics , geometry , computer science , quantum mechanics , universe , operating system , algorithm
The set of all spheres and hyperplanes in the Euclidean space Rn+1 could be identified with the Sitter space Λn+1. All the conformal properties are invariant by the Lorentz form which is natural pseudo-Riemannian metric on Λn+1. We shall study behaviour of some surfaces and foliations as their families using computation in the de Sitter space.