Handan B. ÖZTEKİN and Mahmut ERGÜT, Handan B. Öztekin, Mahmut Ergül

13394

Null mannheim curves in the minkowski 3-space E13

In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E 13. We get the necessary and sufficient conditions for the null Mannheim curves. Then we investigate the null and timelike or spacelike generalized helix as the null Mannheim curve and timelike or spacelike Mannheim partner curve, respectively.
Anahtar Kelimeler:

Mannheim curve, null curve, Minkowski space

Null mannheim curves in the minkowski 3-space E13

In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E 13. We get the necessary and sufficient conditions for the null Mannheim curves. Then we investigate the null and timelike or spacelike generalized helix as the null Mannheim curve and timelike or spacelike Mannheim partner curve, respectively.
Keywords:

Mannheim curve, null curve, Minkowski space,

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  • where c is nonzero constants. From Theorem 3.2, by using the relation κτ = , we obtain differential equation λ (κ)2=−2λcκ2. Solving this equation, we obtain κ τ and κ = 2λe τ , if λc < 0 for some nonzero constant λ and c . Thus, the proposition is proved. In case of spacelike generalized helix is the Mannheim partner curve of some Cartan framed null curve α = α(s) , the proof is similar.
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
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