DOI: 10.3390/axioms12090830 ISSN:
Surface Family Pair with Bertrand Pair as Mutual Curvature Lines in Three-Dimensional Lie Group
Awatif Al-Jedani, Rashad A. Abdel-Baky- Geometry and Topology
- Logic
- Mathematical Physics
- Algebra and Number Theory
- Analysis
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.