Square function estimates for cones over quadratic manifolds

We extend the $L^4$-square function estimates for the parabola and the half-cone to quadratic manifolds in higher dimensions and their conical extensions. To this end, we require transversality for the tangent spaces of the quadratic manifolds at separated points. This allows us to show biorthogonality for the associated system of quadratic equations. For the conical extensions we obtain a wave envelope estimate by High-Low arguments.