Hakan ÖZTÜRK, Özgür BOYACIOĞLU KALKAN, Damla ZEYBEK

3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin TNB*- Smarandache Eğrileri

Bu çalışmada,* spacelike eğrisi  timelike eğrisinin bir involütü olmak üzere * eğrisinin Frenet vektörleri konum vektörleri olarak alındığında null olmayan * * * T N B -Smarandache eğrisinin eğrilik ve burulması  timelike evolüt eğrisine bağlı olarak hesaplanmıştır. Son olarak, elde edilen sonuçlar ile ilgili örnekler verilmiştir.

TNB*-Smarandache Curves of Involute-Evolute Curves In Minkowski 3-space

In this study, the curvature and the torsion of non-null * * * T N B -Smarandache curve are calculated according to the timelike evolute curve  , when the Frenet vectors of the spacelike involute curve *  are taken as the position vectors where *  spacelike curve be the involute of timelike curve  . Finally, illustrative examples related to the results are given.

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Akutagawa, K. and Nishikawa, S., 1990. The gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-Space. Töhoko Mathematical. Journal, 42, 67-82.
Bilici, M. and Çalışkan, M., 2013. On the involutes of spacelike curve with a timelike binormal in Minkowski 3-Space. International Mathematical Forum, 4 (31), 1497-1509.
Bilici, M. and Çalışkan, M., 2011. Some new notes on the involutes of the timelike curves in Minkowski 3-Space. International Journal of Contemporary Mathematical Sciences, 6 (41), 2019-2030.
Bükçü, B. and Karacan, M.K., 2007. On the involute and evolute curves of spacelike curves with a spacelike binormal in Minkowski 3-Space. International Journal of Mathematical. Sciences, 2 (5), 221-232.
Gürses, N., Bektaş, Ö. and Yüce, S., 2016. Special Smarandache curves in 3 R1. Communications Faculty of Sciences. University of Ankara Series. A1 Mathematics and Statics, 65 (2), 143-160.
Hacısalihoğlu, H. H., 1983. Differensiyel Geometri. İnönü Üniversitesi Fen Edebiyat Fakültesi Yayınları, No.2, Malatya, 895s.
Lopez, R., 2014. Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry, 7 (1), 44-107.
Millman, R. S. and Parker, G. D., 1977. Elements of Differential Geometri. Prentice Hall Inc., Englewood Cliffs New Jersey, 275s.
O’Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, London.
Şenyurt, S. and Çalışkan, A., 2015.* * N C -Smarandache curves of Mannheim curve couple according to Frenet frame. International Journal of Mathematical. Combinatorics, 1, 1–13.
Şenyurt, S., Çalışkan, A. and Çelik, Ü., 2016.* * N C - Smarandache curve of Bertrand curves pair according to Frenet frame. International Journal of Mathematical. Combinatorics, 1, 1-7.
Turgut, M., Yılmaz, S., 2008. Smarandache curves in Minkowski space-time. International Journal of Mathematical. Combinatorics, 3, 51-55.
Uğurlu, H.H., 1997. On the geometry of timelike surfaces. Communications Faculty of Sciences. University of Ankara Series. A1 Mathematics and Statics, 46, 211- 223.
Woestijne, V.D.I., 1990. Minimal surfaces of the 3- dimensional Minkowski-space. Proc. Congres Geometrie Differentielle et Applications, Avignon (30 May 1988), Word Scientific Publishing, Geometry and Topology of Submanifolds II, 344-369.