<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

Data publikacji: 20 paź 2015

Zakres stron: 99 - 108

Otrzymano: 01 lis 2012

Przyjęty: 01 mar 2013

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

Słowa kluczowe
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

Data publikacji: 20 paź 2015

Zakres stron: 99 - 108

Otrzymano: 01 lis 2012

Przyjęty: 01 mar 2013

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

Słowa kluczoweGeneral 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.

Słowa kluczowe
General helices, indicatrix, Euclidean 3-spaces, circle