We discuss timelike reflections through spacelike hyperspheres in a de Sitter universe of positive curvature as the natural generalization of timelike reflections through spacelike hyperplanes in the flat Minkowski universe. Taking into account the well-known problem concerning the eigenvalue spectrum of the generator of time displacements in the de Sitter universe we derive equations of motion for linear as well as antilinear operators of motion reversal on spacelike hyperspheres. It is shown that the entire connected component of the homogeneous de Sitter group SO(1,4) may be constructed for either operator.

• Received 5 February 1973

DOI:https://doi.org/10.1103/PhysRevD.9.2710