On the equations of motion in a Riemann space
M. S. Knebelman · Bulletin of the American Mathematical Society · 1945
Introduction.The object of this note is to give a geometric interpretation to the conditions of integrability of Killing's equations 1 and to the similar equations for collineations 2 in an affinely connected space.This is done by considering the more general problem of mapping a space upon itself, the mapping preserving some differential invariant.We shall be concerned with purely local properties so that the functions involved are assumed to have continuous derivatives of any necessary order and the groups are assumed to be infinitesimal.