Minkowski Uzayında Sabit Eğrilikli İnvolüt-Evolüt Eğri Çiftleri için Bazı Karakterizasyonlar

Bu çalışmada, Minkowski uzayında sabit eğrilikli İnvolüt – Evolüt eğri çiftlerine ait pozisyon vektörlerinin karakterizasyonları diferansiyellenebilir fonksiyonlara bağlı olarak elde edilmiştir. Eğri çiftleri Frenet vektör alanlarının Minkowski uzayında sahip olduğu karakterlere göre ayrı ayrı ele alınmıştır. Aynı zamanda bu eğri çiftleri ile ilgili bazı sonuçlar ortaya çıkarılmıştır. Elde edilen bulgular görselleştirilmiş örnekler ile desteklenmiştir.

Some Characterizations for Involute-Evolute Curve Couples with Constant Curvatures in Minkowski Space

In this study, the characterization of position vectors belonging to Involute - Evolute curve pairs with constant curvature in Minkowski space are obtained depending on differentiable functions. The curve couples are investigated according to the characteristics of Frenet vector fields in Minkowski space, separately. At the same time, some conclusions about these pairs of curves were obtained. The findings were supported with visualized samples.

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  • Bayram, E., Bilici, M., 2016. Surface Family with a Common Involute Asymtotic Curve. International Journal of Geometric Methods in Modern Physics, 13, 1-9. Bilici, M., Çalışkan, M., Aydemir, İ., 2002. The Natural Lift Curves and the Geodesic Sprays for the Spherical Indicatrices of the Pair of Evolute-Involute Curves. International Journal of Applied Mathematics, 11, 415-420. Bilici, M., 2011. Natural Lift Curves and the Geodesic Sprays for the Spherical Indicatrices of the Involutes of a Timelike Curve in Minkowski 3Space. International Journal of the Physical Sciences, 6, 4706-4711. Bilici, M., Çalışkan, M., 2009. On the Involutes of the Space-like Curve with a Time-like Binormal in Minkowski 3-Space. International Mathematical Forum, 4, 1497–1509. Bilici, M., Çalışkan, M., 2011. Some New Notes on the Involutes of the Timelike Curves in Minkowski 3-Space. International Journal of Contemporary Mathematical Sciences, 6, 2019-2030. Bilici, M., Çalışkan, M., 2018 . A New Perspective on the Involutes of the Spacelike Curve with A Spacelike Binormal in Minkowski 3-Space. International Mathematical Forum, 4, 14971509. Bilici, M., Çalışkan, M., 2019. 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, 110-119. Bükcü, B., Karacan, M. K., 2007. On The Involute and Evolute Curves of the Timelike Curve in Minkowski 3-Space. Demonstratıo Mathematica, 3, 722-732. Bükcü, B., Karacan, M. K. ,2007. On The Involute and Evolute Curves of Spacelike Curve with a Spacelike Binormal In Minkowski 3-Space. International Journal of Contemporary Mathematical Sciences, 5, 221 – 232. Büyükkütük, S., Öztürk, G., 2015. Constant Ratio Curves According to Bishop Frame in Euclidean 3-Space ?3. General Mathematical Notes, 28, 81-91. Büyükkütük, S. and Öztürk, G., 2015. Constant Ratio Curves According to Parallel Transport Frame in Euclidean 4 Space ?4, New Trends in Mathematical Sciences, 4, 171-178. Chen, B. Y., 2001. Constant Ratio Hypersurfaces. Soochow Journal of Mathematics, 27, 353362. Chen, B.Y., Kim, D.S., Kim, Y.H., 2006. New characterizations of W-curves. Publicatıones Mathematıcae-Debrece, 69, 457–472. Çalışkan, M., Bilici, M., 2002. Some Characterizations for the Pair of InvoluteEvolute Curves in Euclidean space ?3. Bulletin of Pure and Applied Sciences, 21, 289-294. Do Cormo, M. P., 1976, Differential Geometry of Curves and Surfaces, Prentice – Hall, New Jersey, 1-511. Erdoğdu, M., Yavuz, A., 2019. Characterization of Timelike Curves with Constant Curvature Functions. Arabian Journal of Mathematics, In progress. Gürpınar, S., Arslan, K., Öztürk, G. 2014. A Characterization of Constant-Ratio Curves in Euclidean 3-Space ℝ3. arXiv:1410.5577v1 [math.DG], 1-10. Hacısalihoğlu, H. H., 1983. Diferansiyel Geometri. İnönü Üniversitesi Fen Edebiyat Fakültesi Yayınları, No.2, Malatya, 1-895. Özturk, U., Koc Özturk, E.B., Ilarslan, K., 2013. On the Involute-Evolute of the Pseudonull Curve in Minkowski 3-Space. Journal of Applied Mathematics. 651495, 1-6. Öztürk, S., Erdoğdu, M., 2018. Sabit Oranlı İnvolütEvolüt Eğri Çiftleri. Afyon Kocatepe University Journal of Sciences and Engineering, 18, 861-867. Sabuncuoğlu, A., 2014, Diferansiyel Geometri, Nobel, Ankara, Türkiye, 1-514. Şenyurt, S., Bilici, M., Çalışkan, M., 2015. Some Characterization for the Involute Curves in Dual Space. International Journal of Mathematical Combinatorics, 1, 113-125. Walrave, J., 1995. Curves and Surfaces in Minkowski Space. Doctoral thesis, K. U. Leuven, Fac. of Science, Leuven. Yavuz, A., Erdoğdu, M., 2019. Characterization of Spacelike Curves with Constant Curvature Functions. Journal of Geometry and Physics, In progress.