NDLI: A Clifford Algebraic Approach to Line Geometry

Content Provider	Springer Nature Link
Author	Klawitter, Daniel
Copyright Year	2014
Abstract	In this paper we combine methods from projective geometry, Klein’s model, and Clifford algebra. We develop a Clifford algebra whose Pin group is a double cover of the group of regular projective transformations. The Clifford algebra we use is constructed as homogeneous model for the five-dimensional real projective space $${\mathbb {P}^5 (\mathbb{R})}$$ where Klein’s quadric $${M^4_2}$$ defines the quadratic form. We discuss all entities that can be represented naturally in this homogeneous Clifford algebra model. Projective automorphisms of Klein’s quadric induce projective transformations of $${\mathbb {P}^3 (\mathbb{R})}$$ and vice versa. Cayley-Klein geometries can be represented by Clifford algebras, where the group of Cayley-Klein isometries is given by the Pin group of the corresponding Clifford algebra. Therefore, we examine the versor group and study the correspondence between versors and regular projective transformations represented as 4 × 4 matrices. Furthermore, we give methods to compute a versor corresponding to a given projective transformation.
Starting Page	713
Ending Page	736
Page Count	24
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	24
Issue Number	3
e-ISSN	16614909
Language	English
Publisher	Springer Basel
Publisher Date	2014-04-12
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Projective geometry projective transformation null polarity Klein’s quadric Klein’s model Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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