  Different (not only by sign) affine connections are introduced for
contravariant and covariant tensor fields over a differentiable manifold by
means of a non-canonical contraction operator, defining the notion dual bases
and commuting with the covariant and with the Lie-differential operator.
Classification of the linear transports on the basis of the connections between
the connections is given. Notion of relative velocity and relative acceleration
for vector fields are determined. By means of these kinematic characteristics
several other types of notions as shear velocity, shear acceleration, rotation
velocity, rotation acceleration, expansion velocity and expansion acceleration
are introduced and on their basis auto-parallel and non-isotropic (non-null)
vector fields are classified.

General Relativity and Quantum Cosmology