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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Catoni, F., Cannata, R., & Zampetti, P. (2006). An introduction to constant curvature spaces in the commutative (Segre) quaternion geometry. Advances in Applied Clifford Algebras, 16(2), 85 - 101. https://doi.org/10.1007/s00006-006-0010-y