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Dergiler / Mathematical Sciences and Applications E-Notes / 2015 / Cilt: 3 - Sayı: 2

THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3

Melek MASAL
Ayşe Zeynep AZAK
Sayfa
74–83
Yayın Tarihi
2015-10-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also the fundamental forms, geodesic curvatures, normal curvatures and geodesic torsions are calculated and some results are obtained.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We have introduced the ruled surfaces which are generated from the type-2 Bishop vectors.
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Temel Bulgular & Veri:Then, we have calculated Gaussian curvatures, mean curvatures and integral invariants of these surfaces.
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Sonuç & Katkı:Also the fundamental forms, geodesic curvatures, normal curvatures and geodesic torsions are calculated and some results are obtained.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bishop frame · ruled surfaces · Euclidean 3-space

Abstract

We have introduced the ruled surfaces which are generated from the type-2 Bishop vectors. Then, we have calculated Gaussian curvatures, mean curvatures and integral invariants of these surfaces. Also the fundamental forms, geodesic curvatures, normal curvatures and geodesic torsions are calculated and some results are obtained.

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Bu Makaleye Atıf Yap

MASAL, M., AZAK, A. Z. (2015). THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Mathematical Sciences and Applications E-Notes, Cilt: 3 - Sayı: 2, 74–83. https://ajindex.com/articles/690782

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Kaynakça (1)

  1. nces [1] Biran, L., Diferansiyel Geometri Dersleri. ˙Istanbul Universitesi Fen Fak¨ultesi Yayınları. ¨ İstanbul, 1975. [2] Bishop, L. R., There is more than one way to frame a curve. American Mathematical Monthly 82 (1975), no. 3, 246-251. [3] Clauvelin N., Olson W. K., Tobias I., Characterizations of the geometry and topology of DNA pictured as a discrete collection of atoms. Journal of Chemical Theory and Computation 8 (2012), no. 3, 1092-1107. [4] Do Carmo, M. P., Differential Geometry of Curves and Surfaces. Prentice Hall Inc. Englewood Cliffs. New Jersey, 1976. [5] Hacısalihoğlu, H. Hilmi, Diferensiyel Geometri. ˙In¨on¨u Universitesi. Fen-Edebiyat Fak¨ultesi ¨ Yayınları, Malatya, 1983. [6] Han C. Y., Nonexistence of rational rotation-minimizing frames on cubic curves. Computer Aided Geometric Design 25 (2008), no. 4-5, 298-304. [7] Hanson A. J., Ma H., Parallel transport approach to curve framing. Indiana University 425, vol. 11, 1995. [8] Kızıltuğ S., Kaya S., Tarak¸cı O., The slant helices according to type-2 Bishop frame in ¨ Euclidean 3-space. International Journal of Pure and Applied Mathematics 85 (2013), no. 2, 211-222. [9] KızıltuğS., On characterization of inextensible flows of curves according to type-2 Bishop frame in E3. Mathematical and Computational Applications 19 (2014), no. 1, 69-77. [10] Shoeemake K., Animating rotation with quaternion curves. in Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, 245-254, 1985. [11] Özyılmaz E., Classical differential geometry of curves according to type-2 Bishop trihedra. Mathematical and Computational Applications 16 (2011), no. 4, 858-867. [12] Yılmaz S., Turgut M., A new version of Bishop frame and an application to spherical images. Journal of Mathematical Analysis and Applications 371 (2010), 764-776.