TY  - JOUR
T1  - Ortak Bertrand-B İsogeodezik Eğriye Sahip Yüzey Aileleri
TT  - Surface Family With A Common Bertrand-B Isogeodesic Curve
AU  - Şaffak Atalay, Gülnur
AU  - Ayvacı, K. Hilal
PY  - 2020
DA  - September
Y2  - 2020
DO  - 10.21597/jist.696719
JF  - Journal of the Institute of Science and Technology
JO  - J. Inst. Sci. and Tech.
PB  - Iğdır Üniversitesi
WT  - DergiPark
SN  - 2536-4618
SP  - 1975
EP  - 1983
VL  - 10
IS  - 3
LA  - tr
AB  - Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır.Bu çalışmada 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isogeodezik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isogeodezik eğrili yüzey aileleri problemi ele alınmıştır.
KW  - Bertrand-B eğri
KW  - Bishop 2-çatısı
KW  - isogeodezik eğri
KW  - parametrik yüzey
N2  - In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study.In this paper, we construct a surface family possessing a Bertrand B pair of a given curve as an geodesic curve. Using the Bishop-2 frame frame of the given Bertrand B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Bertrand B pairs is both parametric and geodesic on a parametric surface. Finally, we present some interesting examples to show the validity of this study.
CR  - Atalay GŞ, Kasap E,  2016. Surfaces family with common Smarandache geodesic curve according to Bishop frame in Euclidean space, Mathematical Science and Applications E-Notes., 4 , 1.
CR  - Atalay GŞ, E. Kasap,  2017. Surfaces family with common Smarandache geodesic curve, Journal of Science and Arts (JOSA), 4, 41.
CR  - Atalay GŞ, 2018. Surfaces family with a common Mannheim geodesic curve. Journal of Applied Mathematics and Computation, 2(4),155-165.
CR  - Atalay GŞ, 2018. Surfaces family with a common Mannheim asymptotic curve. Journal of Applied Mathematics and Computation, 2(4),145-154.
CR  - Ayvacı KH, 2019. Ortak Mannheim-B İsogeodezikli  ve İsoasimptotikli Yüzey Ailesi, Ondokuz Mayıs Üniversitesi Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi (Basılmış).
CR  - Bayram E, Kasap E, 2014. Hypersurface family with a common isogeodesic, Studies and Research Series Mathematics and Informatics, 24, 2, 12.
CR  - Bertrand J, 1850. Mémoire sur la théorie des courbes à double courbure, Comptes Rendus 36, Journal de Mathématiques Pures et Appliquées 15, 332–350.
CR  - Bishop RL, 1975.  There is more than one way to Frame a curve. The American Mathematical Monthly, 82(3), 246.
CR  - Ergün E, Bayram E,  2016. Surface family with a common natural geodesic lift, Int. J. Math. Combin., 1, 2.
CR  - Kasap E, Akyildiz FT, Orbay K, 2008. A generalization of surfaces family with common spatial geodesic, Applied Mathematics and Computation, 201, 781-789.
CR  - Millman  RS, George DP, 1977. Elements of Differential Geometry, Prentice-Hall.
CR  - O’Neill B, 1966. Elementary Differential Geometry, Academic Press Inc., New York.
CR  - Wang GJ, Tang K, Tai CL, 2004.  Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Des. 36 (5), 447-459.
CR  - Yerlikaya F, Karaahmetoğlu S, Aydemir İ, 2016. On the Bertrand B-Pair Curve in 3-Dimensional Euclidean Space, Journal of Science and Arts, 3(36), 215-224.
CR  - Yılmaz S, Turgut M, 2010. A new version of Bishop frame and an application to spherical images, Journal of Mathematical Analysis and Applications, 371(2), 764-776.
UR  - https://doi.org/10.21597/jist.696719
L1  - https://dergipark.org.tr/tr/download/article-file/988545
ER  -