On quasi focal curves with quasi frame in space
Abstract
In this study, we firstly characterize focal curves by considering quasi frame in the ordinary space. Then, we obtain the relation of each quasi curvatures of curve in terms of focal curvatures. Finally, we give some new conditions with constant quasi curvatures in the ordinary space.
Downloads
References
P. Alegre , K. Arslan, A. Carriazo , C. Murathan and G. Ozturk, Some Special Types of Developable Ruled Surface, Hacettepe Journal of Mathematics and Statistics, 39 (3) (2010), 319-325.
S. Bas and T. Korpınar, A New Characterization of One Parameter Family of Surfaces by Inextensible Flows in De-Sitter 3-Space, Journal of Advanced Physics, 7 (2) (2018), 251-256. https://doi.org/10.1166/jap.2018.1417
L. R. Bishop, There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82 (3) (1975) 246-251. https://doi.org/10.1080/00029890.1975.11993807
M. P. Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey 1976.
M. Dede, C. Ekici, H. Tozak, Directional Tubular Surfaces, International Journal of Algebra, 9 (12) (2015), 527 - 535. https://doi.org/10.12988/ija.2015.51274
T. Korpınar, R. C. Demirkol, A New characterization on the energy of elastica with the energy of Bishop vector fields in Minkowski space. Journal of Advanced Physics. 6(4) (2017), 562-569. https://doi.org/10.1166/jap.2017.1375
T. Korpınar, New type surfaces in terms of B-Smarandache Curves in Sol3 , Acta Scientiarum Technology, 37(2) (2015), 245-250. https://doi.org/10.4025/actascitechnol.v37i3.17425
T. Korpınar, On Velocity Magnetic Curves in Terms of Inextensible Flows in Space. Journal of Advanced Physics. 7(2) (2018), 257-260. https://doi.org/10.1166/jap.2018.1420
T. Korpınar, On the Fermi-Walker Derivative for Inextensible Flows of Normal Spherical Image. Journal of Advanced Physics. 7(2) (2018), 295-302. https://doi.org/10.1166/jap.2018.1428
T. Korpınar, A Note on Fermi Walker Derivative with Constant Energy for Tangent Indicatrix of Slant Helix in the Lie Groups. Journal of Advanced Physics. 7(2) (2018), 230-234. https://doi.org/10.1166/jap.2018.1418
T. Korpınar, A New Version of Normal Magnetic Force Particles in 3D Heisenberg Space, Adv. Appl. Clifford Algebras, 28(4) (2018), 1. https://doi.org/10.1007/s00006-018-0900-9
T. Korpınar, On T-Magnetic Biharmonic Particles with Energy and Angle in the Three Dimensional Heisenberg Group H, Adv. Appl. Clifford Algebras, 28 (1) (2018), 1. https://doi.org/10.1007/s00006-018-0834-2
C. Oniciuc, On the second variation formula for biharmonic maps to a sphere, Publ. Math. Debrecen 61 (2002), 613-622. https://doi.org/10.5486/PMD.2002.2701
E. Turhan, T. Korpınar, Characterize on the Heisenberg Group with left invariant Lorentzian metric, Demonstratio Mathematica 42 (2) (2009), 423-428. https://doi.org/10.1515/dema-2013-0162
E. Turhan, T. Korpınar, On Characterization Of Timelike Horizontal Biharmonic Curves In The Lorentzian Heisenberg Group Heis3 , Zeitschrift f¨ur Naturforschung A- A Journal of Physical Sciences 65a (2010), 641-648. https://doi.org/10.1515/zna-2010-8-904
E. Turhan and T. Korpınar, Parametric equations of general helices in the sol space Sol3 , Bol. Soc. Paran. Mat. 31 (1) (2013), 99-104. https://doi.org/10.5269/bspm.v31i1.15331
R. Uribe-Vargas: On vertices, focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc. 36 (3) (2005), 285-307. https://doi.org/10.1007/s00574-005-0040-4
M. Yeneroglu, T. Korpınar, A New Construction of Fermi-Walker Derivative by Focal Curves According to Modified Frame, Journal of Advanced Physics. 7(2) (2018), 292-294. https://doi.org/10.1166/jap.2018.1425
Copyright (c) 2022 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).
