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A NOTE ON INEXTENSIBLE FLOWS OF CURVES WITH FERMI-WALKER DERIVATIVE IN GALILEAN SPACE G3

  • Received : 2020.06.13
  • Accepted : 2020.09.20
  • Published : 2020.12.25

Abstract

In this paper, Fermi-Walker derivative for inextensible flows of curves are researched in 3-dimensional Galilean space G3. Firstly using Frenet and Darboux frame with the help of Fermi-Walker derivative a new approach for these flows are expressed, then some results are obtained for these flows to be Fermi-Walker transported in G3.

Keywords

References

  1. G. Altay Suroglu, A Modified Fermi-Walker Derivative for Inextensible Flows of Binormal Spherical Image, Open Phys., 16, (2018), 14-20. https://doi.org/10.1515/phys-2018-0003
  2. M.S. Berman, Introduction to general relativistic and scalar-tensor cosmologies, Nova Sciences Publishers. Inc., New York, (2007).
  3. M. Desbrun, and M.P. Cani-Gascuel, Active implicit surface for animation, in: Proc. Graphics Interface-Canadian Inf. Process. Soc., (1998), 143-150.
  4. E. Fermi, Sopra i fenomeni che avvengono in vicinanza di una linea oraria, Atti Accad. Naz. Lincei Cl. Sci. Fiz. Mat. Nat., 31, (1922), 184-306.
  5. M. Gage, and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom., 23, (1986), 69-96. https://doi.org/10.4310/jdg/1214439902
  6. M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26, (1987), 285-314. https://doi.org/10.4310/jdg/1214441371
  7. H. Gun Bozok and M. Ergut, Inextensible Flows of Curves According to Darboux Frame in Galilean Space G3, in: Proc. 4th Int. Conference on Computational Mathematics and Engineering Sciences, (2019), 186-192.
  8. M. Kass, A. Witkin and D. Terzopoulos, Snakes: active contour models, in: Proc. 1st Int. Conference on Computer Vision, (1987), 259-268.
  9. I. Kamenarovic, Existence Theorems for Ruled Surfaces in the Galilean Space G3, Rad HAZU Math. 10, (1991), 183-196.
  10. F. Karakus and Y. Yayli, The Fermi-Walker Derivative in Minkowski space E31, Advances in Applied Clifford Algebras, 27, (2017), 1353-1368. https://doi.org/10.1007/s00006-016-0719-1
  11. T. Korpinar, On the Fermi-Walker Derivative for Inextensible Flows, Z. Naturforsch, 70(7), (2015), 477-482. https://doi.org/10.1515/zna-2015-0044
  12. D.Y. Kwon, F.C. Park and D.P. Chi, Inextensible flows of curves and developable surfaces, Applied Mathematics Letters, 18, (2005), 1156-1162. https://doi.org/10.1016/j.aml.2005.02.004
  13. D. Latifi and A. Razavi, Inextensible flows of curves in Minkowskian Space, Adv. Studies Theor. Phys., 2(16), (2008), 761-768.
  14. H.Q. Lu, J.S. Todhunter and T.W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP,Image Underst., 56, (1993), 265-285.
  15. A.O. Ogrenmis and M. Yeneroglu, Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5(9), (2010), 1424-1427.
  16. H. Oztekin and H. Gun Bozok, Inextensible flows of curves in 4-dimensional Galilean space, Math.Sci. Appl. E-Notes, 1(2), (2013), 28-34.
  17. O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben,(1984).
  18. T. Sahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Mathematica Scientia, 33B(3), (2013), 701-711. https://doi.org/10.1016/S0252-9602(13)60031-4
  19. T. Sahin, F. Karakus and K. Orbay, Parallel Transports with respect to Frenet and Darboux Frames in the Galilean Space, Journal of Science and Arts, 1(50), (2020), 13-24.
  20. D.J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract., 50, (1991), 33-38. https://doi.org/10.1007/BF00032160