  We will extend the concept of electron band Berry curvatures to
superconducting materials. We show that this can be defined for the
Bogoliubov-de Gennes equation describing the superconducting state in a
periodic crystal. In addition, the concept is exploited to understand the
driving mechanism for the optical Kerr effect in time reversal symmetry
breaking superconductors. Finally, we establish a sum rule analogue to the
normal state Hall sum rule making quantitative contact between the imaginary
part of the optical conductivity and the Berry curvature. The general theory
will be applied and tested against the drosophila of the p-wave paired
materials Sr$_2$RuO$_4$.
