Grouptheoretical Characterization of Projective Space and Conformal Space

Extract

In this paper we characterize a projective space and a conformal space, namely a space of inversive geometry of point and sphere, from the standpoint of a homogeneous space. In such spaces a covariant differential of a vectorfield is not a vector, contrary to the case stated in my previous paper “On the vector in homogeneous spaces.” (This journal vol. 5. This paper will be referred to as [1] below.) But when we restrict a rotation about a point to a certain subgroup of the full rotation group, we get a covariant differential which is also a vector, and this situation holds good in a general homogeneous space.