Riemannian manifolds with a generalized axiom of planes

This paper introduces a class of Riemannian manifolds satisfying the axiom of (l, s)-planes that is a generalization of Cartan's axiom of p-planes. The structure of the curvature and Riemannian metric of a manifold with the axiom of (n – 2, n – 1)-planes is established.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 103–110, 1992.