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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/9/830 |
| 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">G</mi></semantics></math></inline-formula>. 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. |
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| ISSN: | 2075-1680 |