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Zbl 1224.53003
Yilmaz, S\" uha; \" Ozyilmaz, Emin; Turgut, Melih
New spherical indicatrices and their characterizations. (English)
[J] An. Ştiinţ. Univ. ``Ovidius" Constanţa, Ser. Mat. 18, No. 2, 337-354 (2010). ISSN 1223-723X; ISSN 1224-1784/e

Summary: We introduce new spherical images by translating Bishop frame vectors of a regular curve to the center of the unit sphere of the three dimensional Euclidean space. Such curves are called Bishop Spherical Indicatrices. The Frenet--Serret apparatus of these new curves is obtained in terms of base curve's Bishop invariants. Additionally, illustrations of two examples are presented.

MSC 2000:: *53A04 Curves in Euclidean space

Keywords: Bishop Frame; spherical images; regular curves; general helix; slant helix; euclidian space

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Zentralblatt MATH Berlin [Germany]