Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Gülnur Şaffak Atalay; Emin Kasap

doi:10.36753/mathenot.421425

EN

Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Abstract

In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the geodesic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache geodesic curve.

Keywords

Bishop frame

References

[1] B. O’Neill, Elementary Differential Geometry, Academic Press Inc., New York, 1966.
[2] M.P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1976.
[3] B. O’Neill, Semi-Riemannian Geometry, Academic Press , New York, 1983.
[4] M. Turgut, and S. Yilmaz, Smarandache Curves in Minkowski Space-time, International Journal of Mathematical Combinatorics, Vol.3, pp.51-55.
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[6] Çetin, M. , Tunçer Y. , Karacan, M.K. , Smarandache Curves According to Bishop Frame in Euclidean Space. arxiv : 1106. 3202v1 [math. DG] , 16 Jun 2011.
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[9] Taşköprü, K. ,and Tosun. M. , Smarandache Curves According to Sabban Frame on . Boletim da Sociedade Paraneanse de Matematica, vol,32, no.1, pp.51-59,2014.
[10] Çetin, M. , and Kocayiğit, H. , On the Quaternionic Smarandache Curves in Euclidean 3-Space. Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 3, 139 – 150.

[11] Deng, B. , 2011. Special Curve Patterns for Freeform Architecture Ph.D. thesis, Eingereicht an der Technischen Universitat Wien, Fakultat für Mathematik und Geoinformation von.
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[15] L. R. Bishop, “There is more than one way to Frame a Curve”, Amer. Math. Monthly 82(3) (1975) 246-251.B. O’Neill, Semi-Riemannian Geometry, Academic Press , New York, 1983.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Gülnur Şaffak Atalay

Emin Kasap

Publication Date

April 15, 2016

Submission Date

August 5, 2015

Acceptance Date

-

Published in Issue

Year 2016 Volume: 4 Number: 1

DOI

https://doi.org/10.36753/mathenot.421425

IZ

https://izlik.org/JA98LZ45BJ

APA

Atalay, G. Ş., & Kasap, E. (2016). Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space. Mathematical Sciences and Applications E-Notes, 4(1), 164-174. https://doi.org/10.36753/mathenot.421425

AMA

1.Atalay GŞ, Kasap E. Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space. Math. Sci. Appl. E-Notes. 2016;4(1):164-174. doi:10.36753/mathenot.421425

Chicago

Atalay, Gülnur Şaffak, and Emin Kasap. 2016. “Surfaces Family With Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space”. Mathematical Sciences and Applications E-Notes 4 (1): 164-74. https://doi.org/10.36753/mathenot.421425.

EndNote

Atalay GŞ, Kasap E (April 1, 2016) Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space. Mathematical Sciences and Applications E-Notes 4 1 164–174.

IEEE

[1]G. Ş. Atalay and E. Kasap, “Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 164–174, Apr. 2016, doi: 10.36753/mathenot.421425.

ISNAD

Atalay, Gülnur Şaffak - Kasap, Emin. “Surfaces Family With Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space”. Mathematical Sciences and Applications E-Notes 4/1 (April 1, 2016): 164-174. https://doi.org/10.36753/mathenot.421425.

JAMA

1.Atalay GŞ, Kasap E. Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space. Math. Sci. Appl. E-Notes. 2016;4:164–174.

MLA

Atalay, Gülnur Şaffak, and Emin Kasap. “Surfaces Family With Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, Apr. 2016, pp. 164-7, doi:10.36753/mathenot.421425.

Vancouver

1.Gülnur Şaffak Atalay, Emin Kasap. Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space. Math. Sci. Appl. E-Notes. 2016 Apr. 1;4(1):164-7. doi:10.36753/mathenot.421425

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Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Abstract

Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

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