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

TitoloAn introduction to constant curvature spaces in the commutative (Segre) quaternion geometry
Tipo di pubblicazioneArticolo su Rivista peer-reviewed
Anno di Pubblicazione2006
AutoriCatoni, F., Cannata R., and Zampetti P.
RivistaAdvances in Applied Clifford Algebras
Volume16
Paginazione85-101
ISSN01887009
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.

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cited By 5

URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-33750191877&doi=10.1007%2fs00006-006-0010-y&partnerID=40&md5=6210d6c04a75d3e68735e0d49dc0669a
DOI10.1007/s00006-006-0010-y
Citation KeyCatoni200685