Multidimensional generalization of a theorem of S. Lie

Abstract

On the basis of several theorems by various authors, we prove the existence in Minkowski space of a nonmetrical hypersurface. For any two connections on this hypersurface, the conditions for conformal and projective congruence are simultaneously fulfilled, which is a new result. The hyper-surface itself has curl by necessity, the differential operators on it have to possess eigenvalues, which leads to the possibility for introducing the concept of spin.