TY  - JOUR
T1  - According to The Frenet Frame Spherical Indicators and Results on E^3
AU  - Yıldırım, Abdullah
AU  - Toktimur, Ali
PY  - 2025
DA  - July
Y2  - 2025
DO  - 10.54974/fcmathsci.1579741
JF  - Fundamentals of Contemporary Mathematical Sciences
JO  - FCMS
PB  - Mustafa UÇKUN
WT  - DergiPark
SN  - 2717-6185
SP  - 123
EP  - 138
VL  - 6
IS  - 2
LA  - en
AB  - In this study, we showed that the spherical indicator curve frames can correspond to a Bishop frame according to the Serret-Frenet frame of a regular curve.
KW  - Serret Frenet Frame
KW  - Bishop Frame
KW  - Spherical Indicator
CR  - Akgün M.A., Frenet curves in 3-dimensıonal contact Lorentzian manifolds, Facta Universitatis, Series:
Mathematics and Informatics, 37(1), 67-76, 2022.
CR  - Ateş F., Kocakuşaklı E., Gök İ., Yaylı Y., A study of the tubular surfaces constructed by the spherical
indicatrices in Euclidean 3-spaces, Turkish Journal of Mathematics, 42(4), 1711-1725, 2018.
CR  - Bilici M., The Curvatures and the Natural Lifts of the Spherical Indicator Curves of the Involute-
Evolute Curve, Master Thesis, Ondokuz Mayıs University, Samsun, Türkiye, 1999.
CR  - Bishop L.R., There is more than one way to frame a curve, The American Mathematical Monthly,
82(3), 246-251, 1975.
CR  - Çapın R., Spherical Indicator Curves in Minkowski Space, Master Thesis, Gaziantep University,
Gaziantep, Türkiye, 2016.
CR  - Erkan E., Yüce S., Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6(12), 321,
2018.
CR  - Frenet J.F., Sur les Fonctions Qui Servent `a D´eterminer L’attraction des Sph´ero¨ıdes Quelconques,
Doctoral Thesis, Chauvin A., 1847.
CR  - Kula L., Yaylı Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation,
169(1), 600-607, 2005.
CR  - Şahin B., Diferansiyel Geometri, Palme Yayınevi, 2021.
CR  - Şenyurt S., Çalışkan Ö.F., The natural lift curves and geodesic curvatures of the spherical indicatrices
of the timelike bertrand curve couple, International Electronic Journal of Geometry, 6(2), 88-99, 2013.
CR  - Şenyurt S., Demet S., Timelike-spacelike Mannheim pair curves spherical indicators geodesic curvatures
and natural lifts, International Journal of Mathematical Combinatorics, 2, 32-54, 2015.
CR  - Yıldırım A., On curves in 3-dimensional normal almost contact metric manifolds, International
Journal of Geometric Methods in Modern Physics, 18(1), 2150004, 2021.
UR  - https://doi.org/10.54974/fcmathsci.1579741
L1  - https://dergipark.org.tr/en/download/article-file/4341630
ER  -