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The Frenet Vector Fields and the Curvatures of the Natural Lift Curve
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The Frenet Vector Fields and the Curvatures of the Natural Lift Curve

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Abstract:

In this paper, Frenet vector fields, curvature and torsion of the natural lift curve of a given curve is calculated by using the angle between Darboux vector field and the binormal vector field of the given curve in 3/1 . Also, a similar calculation is made in 3/1 considering timelike or spacelike Darboux vector field.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 2)
Pages:
38-43
DOI:
https://doi.org/10.18052/www.scipress.com/BSMaSS.2.38
Citation:
E. Ergün et al., "The Frenet Vector Fields and the Curvatures of the Natural Lift Curve", The Bulletin of Society for Mathematical Services and Standards, Vol. 2, pp. 38-43, 2012
Online since:
June 2012
Authors:
Evren Ergün, Mustafa Bilici, Mustafa Çalişkan
Keywords:
Curvature, Frenet Frame, Natural Lift, Torsion
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

Carmo M. P. Do, 1976, Differential Geometry of Curve Surfaces. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

Çalışkan M. Sivridağ A.İ. and Hacısalihoğlu H.H., (1984) Some Characterizationsfor the natural lift curves and the geodesic spray, Communications, Fac. Sci. Univ. Ankara Ser. A Math. 33, Num. 28, 235-242.

Ergün E., Çalışkan M., (2011), On Geodesic Sprays In Minkowski 3-Space, Int. Journal of Contemp. Math. Sciences, Vol. 6, no. 39, 1929-(1933).

O'Neill B., 1967, Elementery Differential Geometry Academic Press, New York and London.

O'Neill B., 1983, Semi-Riemannian Geometry, with applications to relativity. Academic Press, New York.

Ratcliffe J.G., 1994, Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, Inc., New York.

Thorpe J.A., 1979, Elementary Topics In Differential Geometry, Springer-Verlag, New York, Heidelberg-Berlin.

Walrave J., 1995, Curves and Surfaces in Minkowski Space K. U. Leuven Faculteit Der Wetenschappen.

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Cited By:

[1] E. KARACA, M. ÇALIŞKAN, "Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves", GAZI UNIVERSITY JOURNAL OF SCIENCE, p. 1, 2020

DOI: https://doi.org/10.35378/gujs.588496

[2] E. KARACA, M. CALISKAN, "RULED SURFACES AND TANGENT BUNDLE OF PSEUDO-SPHERE OF NATURAL LIFT CURVES", Journal of Science and Arts, Vol. 20, p. 573, 2020

DOI: https://doi.org/10.46939/J.Sci.Arts-20.3-a07

[3] E. ERGÜN, "THE RELATION BETWEEN FRENET FRAME OF THE NATURAL LIFT CURVE AND BISHOP FRAME OF THE CURVE", Journal of Science and Arts, Vol. 21, p. 979, 2021

DOI: https://doi.org/10.46939/J.Sci.Arts-21.4-a09