A new version of energy and elastica for curves with extended darboux frame
DOI:
https://doi.org/10.5269/bspm.51025Resumen
In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on orientable hypersurface in Eâ´. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second kind. Moreover, we have an original and satisfactorily association among energy of the curve on orientable hypersurface in Eâ´.
Referencias
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20. Unluturk Y., Korpınar T. and Cimdiker M., ¨ On k-type pseudo null slant helices due to the Bishop frame in Minkowski 3-space E3 1, AIMS Mathematics, 5(1), 286–299 (2020).
21. Korpınar T. and Unluturk Y., An approach to energy and elastic for curves with extended Darboux frame in Minkowski space, AIMS Mathematics, 5(2), 1025–1034 (2020).
22. Korpinar T., Tangent bimagnetic curves in terms of inextensible flows in space, Int. J. Geom. Methods Mod. Phys. 16 (2), 1950018 (2019).
23. Korpinar T., Optical directional binormal magnetic flows with geometric phase: Heisenberg ferromagnetic model, Optik - International Journal for Light and Electron Optics 219, 165134 (2020).
24. Korpınar, T., Demirkol, R. C., Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold, Journal of Modern Optics 66(8), 857–867 (2019).
25. Korpinar T., A new version of energy for involute of slant helix with bending energy in the Lie groups, Acta Scientiarum. Technology, 41, e36569, 1-8 (2019).
26. Korpinar T., A new version of normal magnetic force particles in 3D Heisenberg space, Adv. Appl. Clifford Algebras, 28:83 (2018).
27. Korpinar T., On T-Magnetic biharmonic particles with energy and angle in the three dimensional Heisenberg group H, Adv. Appl. Clifford Algebras 28:9 (2018).
28. Korpınar, T., Demirkol, R. C., Korpınar, Z., Binormal Schrodinger system of wave propagation field of light radiate in the normal direction with q-HATM approach, Optik - International Journal for Light and Electron Optics, 235 166444 (2021).
29. Korpınar, T., Demirkol, R. C., Curvature and torsion dependent energy of elastica and nonelastica for a lightlike curve in the Minkowski space, Ukrainian Mathematical Journal, 72, 1267–1279 (2021).
2. Gil Medrano O., Relationship between volume and energy of vector fields. Differential Geometry and its Applications. 15, 137–152, (2001).
3. Korpınar T., New characterization for minimizing energy of biharmonic particles in Heisenberg spacetime. Int J Phys. 53, 3208-3218, (2014).
4. Kirchhoff G., Uber das gleichgewicht und die bewegung einer elastichen sc ¨ heibe. Crelles J., 40, 51-88, (1850).
5. Catmull E., Clark J., Recursively generated b-spline surfaces on arbitrary topological surfaces. Computer-Aided Design, 10 (6), (1978).
6. Lopez-Leon T., Koning V., Devaiah K. B. S., Vitelli V., Fernandez-Nieves A. A., Frustrated nematic order in spherical geometries. Nature Phys. 7, 391-394, (2011).
7. Lopez-Leon T., Fernandez-Nieves A. A., Nobili M., Blanc C., Nematic-smectic transition in spherical shells. Phys. Rev. Lett. 106, 247802, (2011).
8. Guven J, Valencia D. M., Vazquez-Montejo J., Environmental bias and elastic curves on surfaces. Phys. A: Math Theory. 47 355201, (2014).
9. Chacon P.M., Naveira A. M., Weston J. M., On the energy of distributions, with application to the quaternionic Hopf fibrations. Monatsh. Math. 133, 281-294, (2001).
10. Asil V., Velocities of dual homothetic exponential motions in D3. Iran. J. Sci. Technol. Trans. A: Sci. 31, 265–271, (2007).
11. Carmo M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey, 1976.
12. Duldul M., Duldul B. U., Kuruoglu N., Ozdamar E., Extension of the Darboux frame into Euclidean 4-space and its invariants, Turk J Math 41, 1628-1639, (2017).
13. Chacon P. M., Naveira A. M., Corrected energy of distrubution on Riemannian manifolds. Osaka J. Math . 41, 97-105, (2004).
14. Altin A., On the energy and pseduoangle of Frenet vector fields in Rn v. Ukranian Mathematical J. 63(6), 969-975, (2011).
15. Korpınar T., Demirkol R. C., Korpınar Z., Soliton propagation of electromagnetic field vectors of polarized light ray traveling along with coiled optical fiber on the unit 2-sphere S 2 . Rev. Mex. Fis. 65(6), 626-633 (2019).
16. Korpınar T., Demirkol R. C., Korpınar Z., Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations. The European Physical Journal D, 73(9), 203 (2019).
17. Korpınar, T., Demirkol, R. C., Korpınar, Z., Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space. International Journal of Geometric Methods in Modern Physics, 16(8), 1950117 (2019).
18. Yeneroglu M., Korpinar T., A new construction of Fermi-Walker derivative by focal curves according to modified frame, Journal of Advanced Physics, 7(2), 292-294 (2018).
19. Korpinar T., Demirkol R. C., Asil V., The motion of a relativistic charged particle in a homogeneous electromagnetic field in De-Sitter space, Revista Mexicana de Fisica 64, 176–180 (2018).
20. Unluturk Y., Korpınar T. and Cimdiker M., ¨ On k-type pseudo null slant helices due to the Bishop frame in Minkowski 3-space E3 1, AIMS Mathematics, 5(1), 286–299 (2020).
21. Korpınar T. and Unluturk Y., An approach to energy and elastic for curves with extended Darboux frame in Minkowski space, AIMS Mathematics, 5(2), 1025–1034 (2020).
22. Korpinar T., Tangent bimagnetic curves in terms of inextensible flows in space, Int. J. Geom. Methods Mod. Phys. 16 (2), 1950018 (2019).
23. Korpinar T., Optical directional binormal magnetic flows with geometric phase: Heisenberg ferromagnetic model, Optik - International Journal for Light and Electron Optics 219, 165134 (2020).
24. Korpınar, T., Demirkol, R. C., Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold, Journal of Modern Optics 66(8), 857–867 (2019).
25. Korpinar T., A new version of energy for involute of slant helix with bending energy in the Lie groups, Acta Scientiarum. Technology, 41, e36569, 1-8 (2019).
26. Korpinar T., A new version of normal magnetic force particles in 3D Heisenberg space, Adv. Appl. Clifford Algebras, 28:83 (2018).
27. Korpinar T., On T-Magnetic biharmonic particles with energy and angle in the three dimensional Heisenberg group H, Adv. Appl. Clifford Algebras 28:9 (2018).
28. Korpınar, T., Demirkol, R. C., Korpınar, Z., Binormal Schrodinger system of wave propagation field of light radiate in the normal direction with q-HATM approach, Optik - International Journal for Light and Electron Optics, 235 166444 (2021).
29. Korpınar, T., Demirkol, R. C., Curvature and torsion dependent energy of elastica and nonelastica for a lightlike curve in the Minkowski space, Ukrainian Mathematical Journal, 72, 1267–1279 (2021).
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Publicado
2022-12-23
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