Characterizations of Loxodromes on Rotational Surfaces in Euclidean 3-Space

Authors : Ferdağ KAHRAMAN AKSOYAK, Burcu BEKTAŞ DEMİRCİ, Murat BABAARSLAN

Pages : 147-159

Doi:10.36890/iejg.1161830

View : 11 | Download : 4

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :In this paper, we study on the characterizations of loxodromes on the rotational surfaces satisfying some special geometric properties such as having constant Gaussian curvature and a constant ratio of principal curvatures insert ignore into journalissuearticles values(CRPC rotational surfaces);. First, we give the parametrizations of loxodromes parametrized by arc-length parameter on any rotational surfaces in $\\mathbb{E}^{3}$ and then, we calculate the curvature and the torsion of such loxodromes. Then, we give the parametrizations of loxodromes on rotational surfaces with constant Gaussian curvature. Also, we investigate the loxodromes on the CRPC rotational surfaces. Moreover, we give the parametrizations of loxodromes on the minimal rotational surface which is a special case of CRPC rotational surfaces. Finally, we give some visual examples to strengthen our main results via Wolfram Mathematica.
Keywords : Loxodrome, curvature, torsion, rotational surface, Gaussian curvature, mean curvature, minimal surfaces, helix, asymptotic curve, Euclidean 3 space