An introduction to constant curvature spaces in the commutative (Segre) quaternion geometry

Francesco Catoni, Roberto Cannata, Paolo Zampetti

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

It is known that complex numbers can be associated with plane Euclidean geometry and their functions are successfully used for studying extensions of Euclidean geometry, i.e., non-Euclidean geometries and surfaces differential geometry. In this paper we begin to study the constant curvature spaces associated with the geometry generated by commutative elliptic-quaternions and we show how the "mathematics" they generate allows us to introduce these spaces and obtain the geodesic equations without developing a complete mathematical apparatus as the one developed for Riemannian geometry. © Birkhäuser Verlag, Basel/Switzerland 2006.
Original languageEnglish
Pages (from-to)85 - 101
Number of pages17
JournalAdvances in Applied Clifford Algebras
Volume16
Issue number2
DOIs
Publication statusPublished - Oct 2006
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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