Normal curves in n-dimensional Euclidean space

Bektas O.

ADVANCES IN DIFFERENCE EQUATIONS, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1186/s13662-018-1922-2
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Normal curve, Curvatures, Explicit solutions, Position vector, 53A04, 53A07, 34A05, EXPLICIT CHARACTERIZATION, RECTIFYING CURVES, TIME-LIKE
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space. We characterize the relationship between the curvatures for any unit speed curve to be congruent to a normal curve in the n-dimensional Euclidean space. Moreover, the differentiable function f ( s) is introduced by using the relationship between the curvatures of any unit speed curve in En. Finally, the differential equation characterizing a normal curve can be solved explicitly to determine when the curve is congruent to a normal curve.