Burmester theory in Cayley–Klein planes with affine base

• Published in: Journal of geometry Vol. 109; no. 3; pp. 1 - 12
• Main Authors: Eren, Kemal, Ersoy, Soley
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-12-2018; Springer Nature B.V
• Subjects: Complex numbers; Euclidean geometry; Geometry; Mathematics; Mathematics and Statistics; Planes; Rigid structures; Instantaneous invariants; 53C42; 53A10; Burmester theory; 53B30; Cayley–Klein planes with affine base
• ISSN: 0047-2468; 1420-8997
• DOI: 10.1007/s00022-018-0450-2

In this paper, we study the Burmester theory in Euclidean, Galilean and pseudo-Euclidean planes and extend the classical Burmester theory to the Cayley–Klein planes with affine base by a unified method. For this purpose, we use the generalized complex numbers and define a generalized form of Bottema’s instantaneous invariants. By this way, we expose the instantaneous geometric properties of motion of rigid bodies in the Cayley–Klein planes with affine base.