An Introduction to Constant Curvature Spaces in the Commutative (Segre) Quaternion Geometry |
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Authors: | Francesco Catoni Roberto Cannata Paolo Zampetti |
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Affiliation: | (1) Centro Ricerche Casaccia, ENEA, Via Anguillarese, 301, 00060 S. Maria di Galeria, Rome, Italy |
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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. |
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