  The aim of this paper is to provide the geometrical structure of a
gravitational field that includes the addition of dark matter in the framework
of a Riemannian and a Riemann--Sasaki spacetime. By means of the classical
Riemannian geometric methods we arrive at modified geodesic equations, tidal
forces, and Einstein and Raychaudhuri equations to account for extra dark
gravity. We further examine an application of this approach in cosmology.
Moreover, a possible extension of this model on the tangent bundle is studied
in order to examine the behavior of dark matter in a unified geometric model of
gravity with more degrees of freedom. Particular emphasis shall be laid on the
problem of the geodesic motion under the influence of dark matter.

General Relativity and Quantum Cosmology