<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

Pubblicato online: 20 ott 2015

Pagine: 99 - 108

Ricevuto: 01 nov 2012

Accettato: 01 mar 2013

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

Parole chiave
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

Pubblicato online: 20 ott 2015

Pagine: 99 - 108

Ricevuto: 01 nov 2012

Accettato: 01 mar 2013

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

Parole chiaveGeneral 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.

Parole chiave
General helices, indicatrix, Euclidean 3-spaces, circle