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

2025/08/04 by Gineli, Ali, Yürük, Hazal, Turgay, Nurettin Cenk
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.11653

Abstract

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.

Citations

• On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone

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