über eine Klasse Riemannscher Mannigfaltigkeiten mit raumartigen pkf-ZusammenhÄngen

One considers m-dimensional Riemannian manifolds M with tangent spaces T_p(M), p ∃M that are a direct sum of a spacelike m-2 plane R_p and a 2-plane H_p. It is supposed that on M there exists a connection whose space-like components are parallel conformal flat (pkf). These components are generated by a vector field X. Assuming that X belongs to a pair X,Y of reciprocal quasi-cocircular vector fields and that the Pfaffian of this pair is the 1-form associated with the connection, the following results are derived: 1. X and Y are of equal constant length (This is true for all Riemannian manifolds). 2. The immersion of the integral manifold of H_p into M is cylindrical and the normal connection is flat. 3. The immersion of any space-like submanifold into M is cylindrical with respect to the sections in H_p and umbilical with respect to all spacelike sections. 4. If m ≤ 4, the integral manifold P_p is flat.