  We study a class of Riemannian manifolds with respect to the covariant
derivative of their curvature tensors. We introduce geometrically the class of
directed Riemannian manifolds of pointwise constant relative sectional
curvature and give a tensor characterization for such manifolds. We prove that
all rotational hypersurfaces are directed and find the rotational hypersurfaces
of pointwise constant relative sectional curvature. For the class of directed
Riemannian manifolds of pointwise constant relative sectional curvature having
a totally umbilical scalar distribution we prove a structural theorem and a
theorem of Schur's type.
