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Math. Comput. Appl. 2011, 16(4), 858-867; doi:10.3390/mca16040858

Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra

Department of Mathematics, Faculty of Science, Ege University, Bornova-Izmir, Turkey
Published: 1 December 2011
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Abstract

In this work, we study classical differential geometry of the curves according to type-2 Bishop trihedra. First, we present some characterizations of a general helix, a helix, special cases and spherical curves. Thereafter, we investigate position vector of a regular curve by a system of ordinary differential equations whose solution gives the components of the position vector with respect to type-2 Bishop frame. Next we prove that the first vector field of the type-2 Bishop frame of a regular curve satisfies a vector differential equation of third order. Solutions of the mentioned system and vector differential equation have not been found. Therefore we present some special characterizations introducing special planes of three dimensional Euclidean space.
Keywords: Classical Differential Geometry; Type-2 Bishop Frame; General Helix; Position Vector; Euclidean Space Classical Differential Geometry; Type-2 Bishop Frame; General Helix; Position Vector; Euclidean Space
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Özyılmaz, E. Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra. Math. Comput. Appl. 2011, 16, 858-867.

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