Principal normal surfaces of generalized null Cartan curves in Minkowski 3-space

Boyuan Xu; Donghe Pei; Boyuan Xu; Donghe Pei

doi:10.3934/math.2026646

AIMS Mathematics

2026, Volume 11, Issue 6: 15716-15724. doi: 10.3934/math.2026646

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Research article

Principal normal surfaces of generalized null Cartan curves in Minkowski 3-space

Boyuan Xu ,
Donghe Pei ^,

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 29 January 2026 Revised: 18 May 2026 Accepted: 26 May 2026 Published: 04 June 2026
MSC : 53A04, 57R45

We define the principal normal surfaces of generalized null Cartan curves in Minkowski 3-space. We give the necessary and sufficient conditions for the relationship between the singularities of these surfaces and the finite type of their base curves. An analogous result does not hold in Euclidean 3-space, where the singularities of the principal normal surface depend also on the torsion of the base curve.
- principal normal surfaces,
- generalized null Cartan curves,
- finite type,
- singularities
Citation: Boyuan Xu, Donghe Pei. Principal normal surfaces of generalized null Cartan curves in Minkowski 3-space[J]. AIMS Mathematics, 2026, 11(6): 15716-15724. doi: 10.3934/math.2026646

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Abstract

We define the principal normal surfaces of generalized null Cartan curves in Minkowski 3-space. We give the necessary and sufficient conditions for the relationship between the singularities of these surfaces and the finite type of their base curves. An analogous result does not hold in Euclidean 3-space, where the singularities of the principal normal surface depend also on the torsion of the base curve.

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