TY  - JOUR
T1  - Characterizations of Loxodromes on Rotational Surfaces in Euclidean 3-Space
AU  - Babaarslan, Murat
AU  - Kahraman Aksoyak, Ferdağ
AU  - Bektaş Demirci, Burcu
PY  - 2023
DA  - April
Y2  - 2023
DO  - 10.36890/iejg.1161830
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 147
EP  - 159
VL  - 16
IS  - 1
LA  - en
AB  - 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 (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.
KW  - Loxodrome
KW  - curvature
KW  - torsion
KW  - rotational surface
KW  - Gaussian curvature
KW  - mean curvature
KW  - minimal surfaces
KW  - helix
KW  - asymptotic curve
KW  - Euclidean 3--space
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UR  - https://doi.org/10.36890/iejg.1161830
L1  - https://dergipark.org.tr/en/download/article-file/2595623
ER  -