<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

Published Online: Oct 20, 2015

Page range: 99 - 108

Received: Nov 01, 2012

Accepted: Mar 01, 2013

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

Keywords
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

Published Online: Oct 20, 2015

Page range: 99 - 108

Received: Nov 01, 2012

Accepted: Mar 01, 2013

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

KeywordsGeneral 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.

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