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This is a Quantitative Study study.

September 24, 2025Open Access

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

Key Points

Classification theorems characterize submanifolds such as pseudo-isotropic and pseudo-umbilical types, clarifying their geometrical properties.
A global frame field on the submanifold is constructed, facilitating the analysis of extrinsic invariants and their geometric significance.
The study focuses on space-like codimension-two submanifolds constrained on the light-like hypercylinder, revealing new classifications.
Characterizations of submanifolds with flat normal bundle enhance understanding of their structures within the Lorentz-Minkowski space.

Abstract

In this paper, we investigate space-like codimension-two submanifolds of the Lorentz-Minkowski space E₁^n+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.

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

Key Points

Abstract

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