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

Authors

FATMA ATEŞ
ERDEM KOCAKUŞAKLI
İSMAİL GÖK
YUSUF YAYLI

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.

DOI

10.3906/mat-1610-101

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