  In this paper, a Riemannian geometry of noncommutative super surfaces is
developed which generalizes [4] to the super case. The notions of metric and
connections on such noncommutative super surfaces are introduced and it is
shown that the connections are metric-compatible and have zero torsion when the
super metric is symmetric, giving rise to the corresponding super Riemann
curvature. The latter also satisfies the noncommutative super analogue of the
first and second Bianchi identities. We also give some examples and study them
in details.
