Abstract
Using a variational principle of Misner’s type, based on a Lobachevsky plane metric treated as a Cayleian metric of the Euclidean plane, Rindler-type motions are analyzed. Within this framework and taking into account the principle of the independence of the simultaneous actions of the fields at a point, it can be replaced by the invariance of the field effects under a certain group and thus a theory of gravity can be formulated to eliminate the intrinsic inconsistencies present in the existing theory.