an:06556917
Zbl 1337.53036
Ergo??du, Melek; ??zdemir, Mustafa
On reflections and rotations in Minkowski 3-space
EN
J. Geom. Symmetry Phys. 39, 1-16 (2015).
00350014
2015
j
53B30 15B10 15A16
Minkowski space; reflections; rotations; matrix representation
Summary: In this paper, we investigate the reflections in Minkowski three-space by three different approach. Firstly, we define Lorentzian reflections with Lorentzian inner product. Then, we examine Lorentzian reflections in view of Lorentzian Householder matrices. Finally, we use pure split quaternions to derive Lorentzian reflections. For each case, we find the matrix representation of Lorentzian reflections and characterize
the plane of reflection by using this matrix representation. Moreover, we prove that any Lorentzian orthogonal transformation can be represented by the composition of at most six reflections.