  It is known that under some transversality and curvature assumptions on the
hypersurfaces involved, the bilinear restriction estimate holds true with
better exponents than what would trivially follow from the corresponding linear
estimates. This subject was extensively studied for conic and parabolic
surfaces with sharp results proved by Wolff and Tao, and with later
generalizations by Lee. In this paper we provide a unified theory for general
hypersurfaces and clarify the role of curvature in this problem, by making
statements in terms of the shape operators of the hypersurfaces involved.
