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It is known that under some transversality and curvature assumptions on thehypersurfaces involved, the bilinear restriction estimate holds true withbetter exponents than what would trivially follow from the corresponding linearestimates. This subject was extensively studied for conic and parabolicsurfaces with sharp results proved by Wolff and Tao, and with latergeneralizations by Lee. In this paper we provide a unified theory for generalhypersurfaces and clarify the role of curvature in this problem, by makingstatements in terms of the shape operators of the hypersurfaces involved.

Optimal bilinear restriction estimates for general hypersurfaces and the role of the shape operator