<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we calculate Frenet frames of the <italic>tangent indicatrix</italic> (<italic>t</italic>), <italic>principal normal indicatrix</italic> (<italic>n</italic>) and <italic>binormal indicatrix</italic> (<italic>b</italic>) of the curve α in ℝ<sup>3</sup> which are spherical curves. Also, we give some differential equations which are characterizations for (<italic>t</italic>), (<italic>n</italic>) and (<italic>b</italic>) to be general helix. Morever we give a characterization for <italic>tangent indicatrix</italic> (<italic>t</italic>) to be a circle.</p></abstract>

In this paper, we calculate Frenet frames of the tangent indicatrix (t), principal normal indicatrix (n) and binormal indicatrix (b) of the curve α in ℝ3 which are spherical curves. Also, we give some differential equations which are characterizations for (t), (n) and (b) to be general helix. Morever we give a characterization for tangent indicatrix (t) to be a circle.

Characterization of Speherical Helices in Euclidean 3-Space

Department of Mathematics, Ankara University, 06100, Ankara, Turkey.

Department of Mathematics, Bilecik Şeyh Edebali University, 11210, Bilecik, Turkey.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Characterization of Speherical Helices in Euclidean 3-Space"}

In this paper, we calculate Frenet frames of the tangent indicatrix (t), principal normal indicatrix (n) and binormal indicatrix (b) of the curve α in ℝ3 which...

Characterization of Speherical Helices in Euclidean 3-Space

Online veröffentlicht: 20. Okt. 2015

Seitenbereich: 99 - 108

Eingereicht: 01. Nov. 2012

Akzeptiert: 01. März 2013

DOI: https://doi.org/10.2478/auom-2014-0035

Schlüsselwörter
General helices, indicatrix, Euclidean 3-spaces, circle

© 2014 Nejat Ekmekci et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Characterization of Speherical Helices in Euclidean 3-Space

Online veröffentlicht: 20. Okt. 2015

Seitenbereich: 99 - 108

Eingereicht: 01. Nov. 2012

Akzeptiert: 01. März 2013

DOI: https://doi.org/10.2478/auom-2014-0035

SchlüsselwörterGeneral helices, indicatrix, Euclidean 3-spaces, circle

© 2014 Nejat Ekmekci et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Schlüsselwörter
General helices, indicatrix, Euclidean 3-spaces, circle