  The concept of time-space defined in an earlier paper of the author is a
certain generalization of the so-called space-time. In this paper we introduce
the concept of time-space manifolds. In the homogeneous case, a time-space
manifold is a differentiable manifold with such tangent spaces which have a
certain fixed time-space structure. We redefine the fundamental concepts of
global relativity theory with respect to this general situation. We study the
concepts of affine connection, parallel transport, curvature tensor and
Einstein equation, respectively.
