The notes on the special tube surfaces generated by normal curves in e4 2
Abstract
In this work, the special tube surfaces generated by normal curves with Frenet frame in Pseudo-Euclidean space E42 are examined and some certain results of describing the surface characterizations on the surfaces are presented in detail. Moreover, using the Gaussian curvatures and mean curvatures of tube surfaces with normal curves generated by Frenet frame in E42, the conditions being Weingarten surface and HK-quadric surface, minimal surface, flat, ... etc are examined in detail.
Downloads
References
Almaz, F., Kulahcı, M.A., The research on rotational surfaces in pseudo Euclidean 4-space with index 2, Acta Mathematica Universitatis Comenianae 92(3), 263 - 280, (2023).
Almaz, F., Kulahcı, M.A., The notes on rotational surfaces in Galilean space, International J. of Geometric Methods in Modern Physic 18(2), (2021).
Almaz, F., Kulahcı, M.A., A Survey on Tube Surfaces in Galilean 3-Space, Journal of Polytechnic 25(3), 1033-1042, (2022).
Almaz, F., Kulahcı, M.A., Some Characterizations on the Special Tubular Surfaces in Galilean Space, Prespacetime Journal 11(7), (2020).
Babadag, F., On The Quaternionic Bertrand Curves In Semi-Euclidean 4-Space E4 2 , International J. of 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., Nesovic, E., Timelike and Null Normal Curves In Minkowski Space E3 1 , Indian J. pure appl. Math. 35(7), 881-888, (2004).
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).
Kim, Y.H., Yoon, D.W., On Non-Developable Ruled Surface in Lorentz Minkowski 3-Spaces, Taiwanese Journal of Mathematics, 11(1), 197-214, (2007).
O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., London, (1983).
Pressley, A., Elementary Differential Geometry. second edition London, UK. Springer-Verlag London Limited, (2010).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).