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.

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