  Fourier restriction conjecture is an important problem in harmonic analysis.
Guo-Oh [17] studied the restriction estimates for quadratic surfaces of
co-dimension 2 in $\mathbb{R}^5$. For one special surface
$(\xi_1,\xi_2,\xi_3,\xi_1^2,\xi_2^2+\xi_1\xi_3)$, they applied a nested
induction argument to build essentially sharp restriction estimate. In this
paper, we simplify their method, and extend it to a variant of the broad-narrow
analysis. As applications, we will prove essentially sharp restriction
estimates for some kinds of degenerate higher co-dimensional quadratic
surfaces.
