?? ? YARI ÖKLİD UZAYINDA NON-NULL NORMAL EĞRİLER
Bu çalışmada, öncelikle non-null eğrilerin temsil formülleri dört boyutlu ?2 4 yarı Öklid uzayında ifade edildi ve ?2 4 'teki nun-null normal eğriler incelenmiş ve normal eğriyi tanımlayıp bazı kesin sonuçlar ayrıntılı olarak ?2 4 'de ifade edilmiştir. Ayrıca, ?2 4 dört boyutlu yarı Öklid uzayında verilen bir eğrinin normal bir eğri olabilmesi için bazı matematiksel koşullar teorem olarak ifade edildi.
NON-NULL NORMAL CURVES IN THE SEMI-EUCLIDEAN SPACE E2^4
In this study, the representation formulas of non-null curves are primarily expressed in four dimensional semi-Euclidean space E24 and the non-null normal curves in E24 are examined and some certain results of describing the nun-null normal curve are presented in detail in E_2^4. In addition, some mathematical conditions are expressed for a curve given in four dimensional semi-Euclidean space E24 to be a nun-null normal curve as theorems.
___
- [1] Almaz, F., Külahcı, M.A., Bektaş, M., “The notes on rotational surfaces in Galilean space”, The Third International Conference on Computational Mathematics and Engineering, Girne, Cyprus, 2018.
- [2] Almaz, F., Külahcı, M.A., “Ivolute-Evolute D-Curves in Minkowski 3-Space ?1 3 ”, Bol. Soc. Paran. Mat., 39(1), 147-156, 2021.
- [3] Almaz, F., Külahcı, M.A., “The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂?2 4 ”, Turkish Journal of Science & Technology, 16(1), 113- 117, 2021.
- [4] Babadag, F., “On The Quaternionic Bertrand Curves in Semi-Euclidean 4-Space ?2 4 ," International J. Research in Engineering and Science, 4(5), 47-50, 2016.
- [5] Grbovic, M., Nesovic, E., “Some relations between rectifying and normal curves in Minkowski 3-space”, Math. Commun., 17, 655-664, 2012.
- [6] Ilarslan, K., Kılıc, N., Erdem, H.A., “Osculating curves in 4-dimensional Semi-Euclidean space with index 2,” Open Math., 15, 562-567, 2017.
- [7] Ilarslan, K., “Spacelike Normal curves in Minkowski space ?1 3 ," Turk J. Math. 29, 53-63, 2015.
- [8] Ilarslan, K., Nesovic, E., “Spacelike and Timelike Normal Curves in Minkowski Space-time," Publications de L’institut Mathematique J. 85(99), 111-118, 2009.
- [9] Kuhnel, W., Differential geometry: curves-surfacesmanifolds, Braunschweig, Wiesbaden 1999.
- [10]Kulahci, M., Almaz, F., “Some Characterizations of osculating Curves in the Lightlike Cone”, Bol. Soc. Paran. Math., 35(2), 39-48, 2017.
- [11]Kulahci, M., Almaz, F., “New Classifications for Spacelike Curves in the Null Cone”, Prespacetime Journal, 7(15), 2002-2014, 2016.
- [12]O’Neill B, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.