Special non-lightlike ruled surfaces in Minkowski 3-space

Chang Sun; Kaixin Yao; Donghe Pei; Chang Sun; Kaixin Yao; Donghe Pei

doi:10.3934/math.20231360

AIMS Mathematics

2023, Volume 8, Issue 11: 26600-26613. doi: 10.3934/math.20231360

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Research article

Special non-lightlike ruled surfaces in Minkowski 3-space

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

Received: 13 July 2023 Revised: 30 August 2023 Accepted: 05 September 2023 Published: 18 September 2023
MSC : 53A05, 57R45

In this paper, we give the existence and uniqueness theorems for non-lightlike framed surfaces and define a special non-lightlike ruled surface in Minkowski 3-space. It may have singularities. We give the conditions for identifying cross-caps and surfaces as developable and maximal. Besides, we demonstrate that if the spacelike ruled surface is developable, then the $ z $-parameter curve is an asymptotic curve if and only if the ruled surface is maximal.
- non-lightlike framed surface,
- cross-cap,
- developable surface,
- maximal surface,
- asymptotic curve
Citation: Chang Sun, Kaixin Yao, Donghe Pei. Special non-lightlike ruled surfaces in Minkowski 3-space[J]. AIMS Mathematics, 2023, 8(11): 26600-26613. doi: 10.3934/math.20231360

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Abstract

In this paper, we give the existence and uniqueness theorems for non-lightlike framed surfaces and define a special non-lightlike ruled surface in Minkowski 3-space. It may have singularities. We give the conditions for identifying cross-caps and surfaces as developable and maximal. Besides, we demonstrate that if the spacelike ruled surface is developable, then the $ z $-parameter curve is an asymptotic curve if and only if the ruled surface is maximal.

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