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Bertrand curves in three dimensional Lie groups
- Source :
- Miskolc Mathematical Notes. 17:999
- Publication Year :
- 2017
- Publisher :
- Mathematical Notes, 2017.
-
Abstract
- In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic curvature function. Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 3.4): A curve ?{\alpha} with the Frenet apparatus {T,N,B,{\kappa},{\tau}} in G is a Bertrand curve if and only if {\lambda}{\kappa}+{\mu}{\kappa}H=1 where {\lambda},{\mu} ? are constants and H is the harmonic curvature function of the curve {\alpha}.<br />Comment: 11 pages. arXiv admin note: substantial text overlap with arXiv:1211.6141, arXiv:1203.1146
- Subjects :
- Mathematics - Differential Geometry
Numerical Analysis
Control and Optimization
Algebra and Number Theory
Frenet–Serret formulas
Mathematics::History and Overview
010102 general mathematics
Mathematical analysis
Curvature function
Lie group
Harmonic (mathematics)
02 engineering and technology
01 natural sciences
Differential Geometry (math.DG)
Metric (mathematics)
Helix
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Discrete Mathematics and Combinatorics
020201 artificial intelligence & image processing
Mathematics::Differential Geometry
0101 mathematics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 17872413 and 17872405
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Miskolc Mathematical Notes
- Accession number :
- edsair.doi.dedup.....2118c6ef596f53529283eb0eca8aa8b8