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Bull. Korean Math. Soc. 2015; 52(3): 963-975

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.963

Copyright © The Korean Mathematical Society.

Some isotropic curves and representation in complex space $\mathbb{C}^{3}$

Jinhua Qian and Young Ho Kim

Northeastern University, Kyungpook National University

Abstract

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In this paper, we give a representation formula for an iso\-tropic curve with pseudo arc length parameter and define the structure function of such curves. Using the representation formula and the Frenet formula, the isotropic Bertrand curve and $k$-type isotropic helices are characterized in the 3-dimensional complex space $\mathbb{C}^{3}$.

Keywords: isotropic curve, isotropic Bertrand curve, $k$-type isotropic helix, pesudo curvature, structure function.

MSC numbers: 53A04, 53B30, 53C40

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