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The natural lift curve of the spherical indicatrix of a non-null curve according to Bishop frame in Minkowski 3-space. (English) Zbl 1503.53038

MSC:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics

References:

[1] R. L. Bishop, There is more than one way to frame a curve. The American Mathematical Monthly, 82:3, 246-251, 1975. · Zbl 0298.53001
[2] J. Walrave, Curves and surfaces in Minkowski space. Doctoral Dissertation, Katholieke Universiteit Leuven Faculteit der Wetenschappen, 147, Belgium, 1995.
[3] J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, Inc., New York, 1994. · Zbl 0809.51001
[4] L. C. B.Silva, Differential geometry of rotation minimizing frames, spherical curves, and quantum mechanics of a constrained particle. Doctoral Dissertation Universidade Federal De Pernambuco, 133, Brazil, 2017.
[5] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press., 1983. · Zbl 0531.53051
[6] G. Arreaga, R. Capovilla ve J. Guven, Frenet-Serret dynamics. Classical Quantum Gravity, 18:23, 5065-5083, 2001. · Zbl 0987.83008
[7] B. Bükcü, M. K. Karacan, On the Slant Helices according to Bishop Frame of the Timelike Curve in Lorentzian Space, Tamkang Journal of Mathematics, 39(3), 255-262, 2008. · Zbl 1168.53306
[8] J. A. Thorpe, Elementary Topics In Differential Geometry, Springer-Verlag, New York, Heidelberg-Berlin, 1979. · Zbl 0404.53001
[9] M. Çalışkan, A. I. Sivridağ and H. H. Hacısalihoğlu, Some Characterizationsfor the natural lift curves and the geodesic spray, Communications, Fac. Sci.Univ. Ankara Ser. A Math. 33, Num. 28,235-242, 1984. · Zbl 0632.53005
[10] E. Ergün, M. Çalışkan, On Geodesic Sprays In Minkowski 3-Space, Int. Journal of. Contemp. Math. Sciences, Vol. 6, no. 39,1929-1933, 2011. · Zbl 1245.53022
[11] E. Ergün, M. Çalışkan, The natural lift curve of the spherical indicatrix of a non-null curve in Minkowski 3-Space, International Mathematical Forum, Vol. 7, no. 15, (2012), 707-717. · Zbl 1248.53015
[12] W. Fenchel, On the differential geometry of closed space curve. Bulletin of the American Mathematical Society, 57, 44-54, (1951). · Zbl 0042.40006
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