A study of the tubular surfaces constructed by thespherical indicatrices in Euclidean $3-$space

Authors

FATMA ATEŞ
ERDEM KOCAKUŞAKLI
İSMAİL GÖK
YUSUF YAYLI

DOI

10.3906/mat-1610-101

Abstract

A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular surfaces with their figures using the program Mathematica.

Keywords

Tubular surface, indicatrix curve, minimal curve

First Page

1711

Last Page

1725

Recommended Citation

ATEŞ, FATMA; KOCAKUŞAKLI, ERDEM; GÖK, İSMAİL; and YAYLI, YUSUF (2018) "A study of the tubular surfaces constructed by thespherical indicatrices in Euclidean $3-$space," Turkish Journal of Mathematics: Vol. 42: No. 4, Article 13. https://doi.org/10.3906/mat-1610-101
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/13