Decoupling for Ruled Hypersurfaces Generated by a Curve

We extend previous work on the two-dimensional developable tangent surface to its higher dimensional analogues M ⊂ Rⁿ⁺¹. The approach here similarly applies cylindrical approximate decoupling at its core, albeit in a new format. However, the presence of additional rulings as n increases necessitates a case-by-case analysis, which in itself reveals interesting aspects of the geometry of M. The contributions of this paper can be viewed as culminating in the optimal ²(Lᵖ) decoupling over Frenet boxes approximating a suitably defined, arbitrarily thin neighborhood of a curve φ.