Clifford algebra and the projective model of Hyperbolic spaces
Andrey Sokolov
TL;DR
This paper explores the use of Clifford algebra within the projective model to analyze hyperbolic spaces across one to three dimensions, building on algebraic frameworks for Cayley-Klein geometries.
Contribution
It applies Clifford algebra techniques to the projective model of hyperbolic spaces, extending algebraic methods to geometric analysis in low dimensions.
Findings
Developed algebraic descriptions of hyperbolic geometries
Connected Clifford algebra with Cayley-Klein models
Provided a framework for geometric computations in hyperbolic spaces
Abstract
I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in [2].
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematics and Applications · Geometric and Algebraic Topology