Normal curves in n-dimensional Euclidean space


Bektas O.

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

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2018
  • Doi Number: 10.1186/s13662-018-1922-2
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Normal curve, Curvatures, Explicit solutions, Position vector, 53A04, 53A07, 34A05, EXPLICIT CHARACTERIZATION, RECTIFYING CURVES, TIME-LIKE
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

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.