Acta mathematica scientia, Series B >
INTRINSIC EQUATIONS FOR A GENERALIZED RELAXED ELASTIC LINE ON AN ORIENTED SURFACE IN THE GALILEAN SPACE
Received date: 2011-11-07
Revised date: 2012-05-05
Online published: 2013-05-20
In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.
Tevfik SAHIN . INTRINSIC EQUATIONS FOR A GENERALIZED RELAXED ELASTIC LINE ON AN ORIENTED SURFACE IN THE GALILEAN SPACE[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 701 -711 . DOI: 10.1016/S0252-9602(13)60031-4
[1] C¸ ¨oken A C, Y¨ucesan A, Ayy?ld?z N, Manning G S. Relaxed elastic line on a curved pseudo-hypersurface in
pseudo-Euclidean spaces. J Math Anal Appl, 2006, 315: 367–378
[2] G¨org¨ul¨u A, Ekici C. Intrinsic equations for a generalized relaxed elastic line on an oriented surface. Hacettepe Journal of Math and Statistics, 2010, 39(2): 197–203
[3] Landau L D, Lifshitz E M. Theory of Elasticity. Oxford: Pergamon Press, 1979: 84
[4] Manning G S. Relaxed elastic line on a curved surface. Quart Appl Math, 1987, 45(3): 515–527
[5] Nickerson H K, Manning G S. Intrinsic equations for a relaxed elastic line on an oriented surface. Geometriae
dedicate, 1988, 27: 127–136
[6] ¨Unan Z, Y?lmaz M. Elastic lines of second kind on an oriented surface. Ondokuz May?s ¨Univ Fen dergisi, 1997, 8(1): 1–10
[7] Y?lmaz M. Some relaxed elastic line on a curved hypersurface. Pure Appl Math Sci, 1994, 39: 59–67
[8] Ekici C, G¨org¨ul¨u A. Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the
Minkowski 3-space E3 1. Turkish J Math, 2009, 33: 397–407
[9] G¨urb¨uz N. Intrinsic formulation for elastic line deformed on a surface by external field in the Minkowski 3-space E3 1. J Math Anal Appl, 2007, 327: 1086–1094
[10] Tutar A, Sar?o?glugil A. Relaxed elastic lines of second kind on oriented surface in Minkowski space. App Math Mech, 2006, 27(11): 1481–1489
[11] Hilbert D, Cohn-Vossen S. Geometry and Imagination. New York: Chelsea, 1952
[12] Cox D, Little J, O’shea D. Ideals, Variets, and Algorithms. Second Edition. New York: Springer-Verlag, 1997: 349–362
[13] Molnar E. The projective interpretation of the eight 3-dimensional homogeneous geometries. Beitr Algebra Geom, 1997, 38: 261–288
[14] Casse R. Projective Geometry: An Introduction. Oxford Univ Press, 2006: 45–51
[15] Pavkoviˇc B J, Kamenaroviˇc I. The equiform differential geometry of curves in the Galilean space G3. Glas
Mat, 1987, 22(42): 449–457
[16] Yaglom I M. A Simple Non-Euclidean Geometry and Physical Basis. New York: Springer-Verlag, 1979
[17] R¨oschel O. Die Geometrie des Galileischen Raumes. Habilitationssch, Inst f¨ur Mat und Angew Geometrie, 1984
[18] S¸ahin T, Y?lmaz M. The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space. Acta Math Hungar, 2011, 132(1/2): 154–167
[19] S¸ahin T, Y?lmaz M. On singularities of the Galilean spherical darboux ruled surface of a space curve in G3.
Ukrainian Math J, 2011, 62(10): 1377–1387
[20] Capovilla R. Chryssomalakos C, Guven J. Hamiltonians for curves. J Phys A: Math Gen, 2002, 35: 6571–6587
[21] Langer J. Recursion in Curve Geometry. New York J Math, 1999, 5: 25–51
[22] Do Carmo M P. Differential Geometry of Curves and Surfaces. New Jerse: Prentice-Hall, 1976
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