Highly incidental patterns on a quadratic hypersurface in R4

By a suitable projection from this quadratic hypersurface onto R3, we obtain m points and n lines in R3, with at most s=O(1) lines on a common plane, such that the number of incidences between the m points and the n lines is Θ(m2∕3n1∕2). It remains an interesting question to determine if this bound is also tight in general.