On Involutes of Admissible Non-Lightlike Curves in Pseudo-Galilean 3-Space

This paper aims to investigate the theory of involutes of admissible non-lightlike curves in pseudo-Galilean 3- space. In the second section of this paper, we give fundamental concepts of pseudo-Galilean 3-space and curves over this space together with their casual properties. In section three, the involute of admissible non-lightlike curves in pseudo-Galilean 3-space is defined. Furthermore, the properties of involutes of admissible non-lightlike curves are also investigated by applying the fundamental properties provided in section 2. In the last part but not least, we give some numerical examples as applications of the theorems and corollaries which are derived in the previous section.

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[1] Carmo M.P.D., Differential Geometry of Curves and Surfaces, Canada: Dover Publication Inc., 2016.
[2] Divjak B., Curves in Pseudo-Galilean Geometry, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, 41 (1998) 117-128.
[3] Divjak B., The Equiform Differential Geometry of Curves in the Pseudo-Galilean Space, Mathematical Communications, 13(2) (2008).
[4] Divjak B., Sipus M.Z., Some Special Surfaces in the Pseudo- Galilean space. Acta Mathematica Hungarica, 118 (2008) 209-226.
[5] Elzawy M., Mosa M., Helicoidal Surfaces in Galilean Space with Density, Frontiers in Physics, 8 (2020) 1-6.
[6] Fock V., The Theory of Space, Time and Gravitation. 2nd ed. England: Pergamon Press, 1964.
[7] Fuchs T., Evolutes and Involutes of Spatial Curve. The American Mathematical Monthly, 120 (2013) 217-231.
[8] Lipschutz M.M., Schaum’s Outline of Differential Geometry, Canada: McGraw Hill, 1969.
[9] Merbach U.C., Boyer C.B., A history of Mathematics, New Jersey: John Wiley and Sons Inc., 2011.
[10] Saad M.K., Spacelike and Timelike Admissible Smarandache Curves in Pseudo-Galilean Space, Journal of the Egyptian Mathematical Society, 24(3) (2016) 416-423.
[11] Sahin T., Intrinsic Equations for a Generalized Relaxed Elastic Line on an Oriented Surface in the Galilean Space, Acta Math. Sci., 33(3) (2013) 701-711.
[12] Sipus M.Z., Divjak B., Surfaces of Constant Curvature in the Pseudo-Galilean Space, International Journal of Mathematics and Mathematical Sciences, 2012 (2012) 1- 28.
[13] Tuncer Y., Canal Surface in Galilean 3-Space, Kyungpook Mathematical Journal, 57(2) (2017) 319-326.
[14] Yuzbasi Z.K., Yoon D.W., Geometry of Isophote Curves in Galilean Space, AIMS Mathematics, 6(1) (2021) 66-76.