Codimensions-Two Submanifolds Contained in the Light-like Hypercylinder LCⁿ× R

In this paper, we investigate space-like codimension-two submanifolds of the Lorentz-Minkowski space E₁ⁿ⁺² constrained to lie on the light-like hypercylinder LCⁿ × R over the light cone LCⁿ. By constructing a geometrically defined global frame field on the submanifold, we analyze the geometric interpretations of the associated extrinsic invariants by providing characterizations of (pseudo-)isotropic and pseudo-umbilical submanifolds, as well as submanifolds with flat normal bundle. In particular, we obtain local classification theorems for these classes of submanifolds.