A Survey on Timelike-Spacelike Involute-Evolute Curve Pair

Yıl 2023, , 49 - 57, 31.03.2023

Mustafa Bilici

https://doi.org/10.18185/erzifbed.1129800

Cited By: 1

Öz

A Survey on Timelike-Spacelike Involute-Evolute Curve Pair

Öz

This paper concentrates on the requirements of being an integral curve for the geodesic spray of the natural lift curves of spherical indicatrices of the timelike-spacelike involute-evolute curve pair in Lorentz 3-space. In addition, the obtained results were supported by one example.

Anahtar Kelimeler

Involute-evolute curve pair, Lorentz space, geodesic spray, spherical indicatrix, natural lift curve.

Kaynakça

• Millman, R. S., Parker, G. D., Elements of Differential Geometry, Prentice-Hall Inc., Englewood Cliffs Press, New Jersey, 1977.
• Hacısalihoğlu H. H., Differantial Geometry, Ankara University Faculty of Science Press, Ankara, 2000.
• Çalışkan, M., Bilici, M., Some Characterizations for the Pair of Involute-Evolute Curves in Euclidean Space , Bull. of Pure and Appl. Sci., 21 (2002), 2, pp. 289-294.
• Thorpe, J. A., Elemantary Topics In Differantial Gemetry, Springer-Verlag, New York, Heidelberg-Berlin, 1979.
• Çalışkan, M., Sivridağ, A.İ., Hacısalihoğlu. H. H., Some Characterizations For The Natural Lift Curves and The Geodesic Spray, Commun. Fac. Sci. Ank. Series A1, 33 (1984), pp. 235-242.
• Bilici, M., Çalışkan, M., Aydemir, İ., The Natural Lift Curves and the Geodesic Sprays for the Spherical Indicatrices of the Pair of Evolute-Involute Curves, Int. J. of Appl. Math., 11 (2003), 4, pp. 415-420.
• Bilici, M., Natural Lift Curves and the Geodesic Sprays for the Spherical Indicatrices of the Involutes of a Timelike Curve in Minkowski 3- space. International Journal of the Physical Sciences, 6 (2011) pp. 4706-4711.
• Bilici, M., Ahmad, T. A., On the Natural Lift Curves for the Involute Spherical Indicatrices in Minkowski 3-space. Malaya Journal of Matematik, 5 (2017), 2, pp. 407-415.
• Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in , International Journal of the Physical Sciences, 7 (2012), 16, pp. 2414-2421.
• Ali, A.T., New special curves and their spherical indicatrix, Glob. J. Adv. Res. Class. Mod. Geom., 1 (2012), 2, pp. 28-38.
• İyigün, E, The tangent spherical image and ccr-curve of a time-like curve in , J. Inequal. Appl., 55 (2013), pp. 1-5.
• Bilici, M., Ergün, E., Çalişkan, M., The natural lift curves for the spherical indicatrices of spacelike Bertrand couple in Minkowski 3-space, J. Math. Comput. Sci. 4 (2014), 1, pp. 85-104.
• Bilici, M., Çalışkan, M., Some Geometrical Calculations for the Spherical Indicatrices of Involutes of a Timelike Curve in Minkowski 3-Space, Journal of Advances in Mathematıcs 5 (2014), 2, pp. 668-677.
• Bilici, M., Ergün, E., Çalıskan, M., A New Approach to Natural Lift Curves of The Spherical Indicatrices of Timelike Bertrand Mate of a Spacelike Curve in Minkowski 3-Space, International Journal of Mathematical Combinatorics 1 (2015), pp. 35-48.
• Bilici, M., Çalışkan, M., Some new results on the curvatures of the spherical indicatrices of the involutes of a spacelike curve with a spacelike binormal in Minkowski 3-space, MathLAB Journal, 2 (2019), 1, pp. 110-119.
• Bilici, M., Çalışkan, M., A new perspective on the involutes of the spacelike curve with a spacelıke binormal in Minkowskı 3-space, Journal of Science and Arts, 18 (2018), 3, pp. 573-582.
• Ali, A. T., Lopez, R., Slant helices in Minkowski space . Journal of the Korean Mathematical Society, 48 (2011), 1, pp. 159–167.
• O’neill, B., Semi Riemann Geometry, Academic Press, New York, London, 1983.
• Woestijne, V. D. I., Minimal Surfaces of the 3-dimensional Minkowski space. Word Scientific Publishing. Singapore, pp 344-369, 1990.
• Bilici, M., On the timelike or spacelike involute-evolute curve couples, Ph.D. thesis, Ondokuz Mayıs University, Samsun, Turkey, 2009.