Surface Family Pair with Bertrand Pair as Mutual Curvature Lines in Three-Dimensional Lie Group

This paper is on deducing the necessary and sufficient conditions of a surface family pair with a Bertrand pair as mutual curvature lines in three-dimensional Lie group G. As a result, the consequence for the ruled surface family pair is also extrapolated. Meanwhile, examples are specified to show t...

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Bibliographic Details
Published inAxioms Vol. 12; no. 9; p. 830
Main Authors Al-Jedani, Awatif, Abdel-Baky, Rashad A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2023
Subjects
Bertrand pair
Curvature
Curves
Lie groups
marching-scale functions
Mathematical research
Serret–Frenet formulae
Saudi Arabia
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Summary:This paper is on deducing the necessary and sufficient conditions of a surface family pair with a Bertrand pair as mutual curvature lines in three-dimensional Lie group G. As a result, the consequence for the ruled surface family pair is also extrapolated. Meanwhile, examples are specified to show the surface family with common Bertrand geodesic curves.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12090830