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Dergiler / Journal of Universal Mathematics / 2026 / Cilt: 2 Sayı: 1

INEXTENSIBLE FLOWS OF CURVES ACCORDING TO SABBAN FRAME IN GALILEAN SPACE G3

Hülya Gün Bozok(OSMANİYE KORKUT ATA UNIVERSITY)
Sayfa
75–81
Yayın Tarihi
2019-01-30
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also inextensible curve ow are expressed as a partial dierential equation involving geodesic curvature according to this frame.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper inextensible ows of curves in 3-dimensional Galilean space is researched.
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Temel Bulgular & Veri:Firstly Sabban frame is dened in 3-dimensional Galilean space, then necessary and sucient conditions for inextensible ows of curves with Sabban frame in 3-dimensional Galilean space are given.
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Sonuç & Katkı:Also inextensible curve ow are expressed as a partial dierential equation involving geodesic curvature according to this frame.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Inextensible ows · Sabban Frame · Inextensible ows

Abstract

In this paper inextensible ows of curves in 3-dimensional Galilean space is researched. Firstly Sabban frame is dened in 3-dimensional Galilean space, then necessary and sucient conditions for inextensible ows of curves with Sabban frame in 3-dimensional Galilean space are given. Also inextensible curve ow are expressed as a partial dierential equation involving geodesic curvature according to this frame.

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Bu Makaleye Atıf Yap

Bozok, H. G. (2019). INEXTENSIBLE FLOWS OF CURVES ACCORDING TO SABBAN FRAME IN GALILEAN SPACE G3. Journal of Universal Mathematics, Cilt: 2 Sayı: 1, 75–81. https://doi.org/10.33773/jum.506493

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Kaynakça (12)

  1. A. O. Oğrenmis, M. Bektaş, M. Ergut, On the helices in the Galilean space G3, Iranian Journal of science & Technology, Transaction A, 31, 177-181, (2007).
  2. A. O. Oğrenmis, M. Yenero_glu, Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5(9),1424-1427,(2010).A. O. Oğrenmis, On curvatures of a frenet curve in the pseudo-Galilean space G31 Inter. J. Phys.Sci. 5, 2363-2365, (2010).B. Divjak and M. Sipus, Some special surfaces in the pseudo-Galilean space,Acta Math. Hungar. 118, 209-229,(2008).
  3. D. Y. Kwon, FC. Park, DP Chi, Inextensible ows of curves and developable surfaces, Applied Mathematics Letters 18, 1156-1162, (2005).
  4. D.Y. Kwon, F.C. Park,, Evolution of inelastic plane curves, Appl. Math. Lett., 12,115-119, (1999).D.J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract. 50, 33-38, (1991). D. Lati_, A. Razavi, Inextensible ows of curves in Minkowskian Space, Adv. Studies Theor. Phys. 2(16), 761-768, (2008).E. Molnar, The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 38 (2), 261-288, (1997).G. Chirikjian, J. Burdick, A modal approach to hyper-redundant manipulator kinematics, IEEE Trans. Robot. Autom. 10,343-354, (1994).H. Oztekin and H. Gün Bozok, Inextensible ows of curves according to Sabban frame in pseudo-Galilean space G13, i-managers Journal on Mathematics, Vol.2, N.1, pp.1-12, (2013).H. Mochiyama, E. Shimemura, H. Kobayashi, Shape control of manipulators with hyper degrees of freedom, Int. J. Robot.Res.,18, 584-600, (1999).H.Q. Lu, J.S. Todhunter, T.W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP,Image Underst. 56, 265-285, (1993).I.M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, (1979).I. Kamenarovic, Existence Theorems for Ruled Surfaces in the Galilean Space G3. Rad HAZU Math. 10, 183-196,(1991).J. Koenderink, Solid shape, MIT Press,
  5. Cambridge, MA, (1990).M. Ergut, E. Turhan, T. Körpinar, Characterization of inextensible ows of spacelike curves with Sabban frame in S2 1, Bol. Soc. Paran. Mat. 31(2), 47-53, (2013).M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, in: Proc. 1st Int. Conference on Computer Vision, 259-268 (1987).M. Desbrun, M.-P. Cani-Gascuel, Active implicit surface for animation, in: Proc. Graphics Interface-Canadian Inf. Process. Soc., 143-150, (1998).
  6. O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, (1984).Z. M. Sipus, Ruled Weingarten surfaces in the Galilean space, Periodica Mathematica Hungarica, 56(2), 213-225, (2008).
  7. A. O. Oğrenmis, M. Bektaş, M. Ergut, On the helices in the Galilean space G3, Iranian Journal of science & Technology, Transaction A, 31, 177-181, (2007).
  8. A. O. Oğrenmis, M. Yenero_glu, Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5(9),1424-1427,(2010).A. O. Oğrenmis, On curvatures of a frenet curve in the pseudo-Galilean space G31 Inter. J. Phys.Sci. 5, 2363-2365, (2010).B. Divjak and M. Sipus, Some special surfaces in the pseudo-Galilean space,Acta Math. Hungar. 118, 209-229,(2008).
  9. D. Y. Kwon, FC. Park, DP Chi, Inextensible ows of curves and developable surfaces, Applied Mathematics Letters 18, 1156-1162, (2005).
  10. D.Y. Kwon, F.C. Park,, Evolution of inelastic plane curves, Appl. Math. Lett., 12,115-119, (1999).D.J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract. 50, 33-38, (1991). D. Lati_, A. Razavi, Inextensible ows of curves in Minkowskian Space, Adv. Studies Theor. Phys. 2(16), 761-768, (2008).E. Molnar, The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 38 (2), 261-288, (1997).G. Chirikjian, J. Burdick, A modal approach to hyper-redundant manipulator kinematics, IEEE Trans. Robot. Autom. 10,343-354, (1994).H. Oztekin and H. Gün Bozok, Inextensible ows of curves according to Sabban frame in pseudo-Galilean space G13, i-managers Journal on Mathematics, Vol.2, N.1, pp.1-12, (2013).H. Mochiyama, E. Shimemura, H. Kobayashi, Shape control of manipulators with hyper degrees of freedom, Int. J. Robot.Res.,18, 584-600, (1999).H.Q. Lu, J.S. Todhunter, T.W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP,Image Underst. 56, 265-285, (1993).I.M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, (1979).I. Kamenarovic, Existence Theorems for Ruled Surfaces in the Galilean Space G3. Rad HAZU Math. 10, 183-196,(1991).J. Koenderink, Solid shape, MIT Press,
  11. Cambridge, MA, (1990).M. Ergut, E. Turhan, T. Körpinar, Characterization of inextensible ows of spacelike curves with Sabban frame in S2 1, Bol. Soc. Paran. Mat. 31(2), 47-53, (2013).M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, in: Proc. 1st Int. Conference on Computer Vision, 259-268 (1987).M. Desbrun, M.-P. Cani-Gascuel, Active implicit surface for animation, in: Proc. Graphics Interface-Canadian Inf. Process. Soc., 143-150, (1998).
  12. O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, (1984).Z. M. Sipus, Ruled Weingarten surfaces in the Galilean space, Periodica Mathematica Hungarica, 56(2), 213-225, (2008).