  In this paper, we use the notion of super tangent bundle for a space-time
manifold, and use super metrics on it to model gravity and some types of matter
that is the source of the gravity and can be interpreted as dark matter. In
this view, gravity is an effect of the symmetric part of the super metric and
dark matter is an effect of the symplectic part of the super metric. So, dark
matter can be considered as a result of the odd part of the super space-time.
We use variation of the Hilbert action to derive field equations for
interaction of gravity and matter and investigate some of the results. We also
construct some solution for these equations.
