NON-NULL NORMAL CURVES IN THE SEMI-EUCLIDEAN SPACE E2^4

Year 2021, , 137 - 140, 29.06.2021

Fatma Almaz , Mihriban Alyamac Kulahci

https://doi.org/10.22531/muglajsci.852180

Abstract

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.

Keywords

frenet frame, normal curve, Semi-Euclidean space E2 4

Thanks

The authors wish to express their thanks to the authors of literatures for the supplied scientific aspects and idea for this study.

References

• 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.
• Almaz, F., Külahcı, M.A., “Ivolute-Evolute D-Curves in Minkowski 3-Space E_1^3”, Bol. Soc. Paran. Mat., 39(1), 147-156, 2021.
• Almaz, F., Külahcı, M.A., “The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E_2^4”, Turkish Journal of Science & Technology, 16(1), 113-117, 2021.
• Babadag, F., “On The Quaternionic Bertrand Curves in Semi-Euclidean 4-Space E_2^4," International J. Research in Engineering and Science, 4(5), 47-50, 2016.
• Grbovic, M., Nesovic, E., “Some relations between rectifying and normal curves in Minkowski 3-space”, Math. Commun., 17, 655-664, 2012.
• Ilarslan, K., Kılıc, N., Erdem, H.A., “Osculating curves in 4-dimensional Semi-Euclidean space with index 2,” Open Math., 15, 562-567, 2017.
• Ilarslan, K., “Spacelike Normal curves in Minkowski space E_1^3," Turk J. Math. 29, 53-63, 2015.
• Ilarslan, K., Nesovic, E., “Spacelike and Timelike Normal Curves in Minkowski Space-time," Publications de L’institut Mathematique J. 85(99), 111-118, 2009.
• Kuhnel, W., Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden 1999.
• Kulahci, M., Almaz, F., “Some Characterizations of osculating Curves in the Lightlike Cone”, Bol. Soc. Paran. Math., 35(2), 39-48, 2017.
• Kulahci, M., Almaz, F., “New Classifications for Space-like Curves in the Null Cone”, Prespacetime Journal, 7(15), 2002-2014, 2016.
• O’Neill B, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.