In this paper, we define a new family of curves and call it a familyof similar curves with variable transformation or briefly SA-curves. Also weintroduce some characterizations of this family and we give some theorems.This definition introduces a new classification of a space curve. Also, we usethis definition to deduce the position vectors of plane curves, general helicesand slant helices, as examples of a similar curves with variable transformation
A.T. Ali and M. Turgut, Position vector of a time-like slant helix in Minkowski 3-space, J. Math. Anal. Appl. 365 (2010) 559–569.
A.T. Ali, Position vectors of spacelike general helices in Minkowski 3-space, Nonl. Anal. Theory Meth. Appl. 73 (2010) 1118–1126.
A.T. Ali, Position vectors of general helices in Euclidean 3-space, Bull. Math. Anal. Appl. 3(2), (2010), 198–205.
A.T. Ali, Position vectors of slant helices in Euclidean 3-space, J. Egyptian Math. Soc. 20, (2012), 1–6.
M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997), 1503–1509.
C. Boyer, History of Mathematics, Wiley, New york, 1968.
C. Camci, K. Ilarslan, L. Kula and H.H. Hacisalihoglu, Harmonic curvatures and generalized helices in En, Chaos, Solitons and Fractals 40 (2009), 2590–2596.
L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn and Co., 1909.
H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73 (1996), 699–704.
H.H. Hacisalihoglu, Differential Geometry, Ankara University, Faculty of Science Press, 2000. [14] S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004), 531–537.
W. Kuhnel, Differential Geometry: Curves - Surfaces - Manifolds, Wiesdaden: Braunchweig; 1999. [16] L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comp. 169 (2005), 600–607.
L. Kula, N. Ekmekci, Y. Yayli and K. Ilarslan, Characterizations of slant helices in Euclidean 3-space, Tur. J. Math. 33 (2009), 1–13.
M.M. Lipschutz, Schum,s Outline of Theory and Problems of Differential Geometry, McGraw-Hill Book Company, New York, 1969.
R.S. Milman and G.D. Parker, Elements of Differential Geometry, Prentice-Hall Inc., Engle- wood Cliffs, New Jersey, 1977.
J. Monterde, Curves with constant curvature ratios, Bulletin of Mexican Mathematic Society, 3a serie vol. 13 (2007), 177–186.
J. Monterde, Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. Design 26 (2009), 271–278.
M. Petrovic-Torgasev and E. Sucurovic, W-curves in Minkowski space-time, Novi Sad J. Math. 32(2) (2002), 55–65.
E. Salkowski, Zur transformation von raumkurven, Mathematische Annalen 66 (1909), 517– 557. [24] P.D. Scofield, Curves of constant precession, Amer. Math. Monthly 102 (1995), 531–537.
D.J. Struik, Lectures in Classical Differential Geometry, Addison,-Wesley, Reading, MA, 1961. [26] M. Turgut and S. Yilmaz, Contributions to classical differential geometry of the curves in E3, Scientia Magna 4 (2008), 5–9.
1- Mathematics Department, Faculty of Science, Minia University, Minia, Egypt.
2- Al-Azhar University, Faculty of Science, Mathematics Department, Nasr City, 11884, Cairo, Egypt.
3- King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah, 21589, Saudi Arabia.
E-mail address: elsabbaghmostafa@yahoo.com and atali71@yahoo.com
Year 2013,
Volume: 1 Issue: 2, 80 - 90, 01.12.2013
A.T. Ali and M. Turgut, Position vector of a time-like slant helix in Minkowski 3-space, J. Math. Anal. Appl. 365 (2010) 559–569.
A.T. Ali, Position vectors of spacelike general helices in Minkowski 3-space, Nonl. Anal. Theory Meth. Appl. 73 (2010) 1118–1126.
A.T. Ali, Position vectors of general helices in Euclidean 3-space, Bull. Math. Anal. Appl. 3(2), (2010), 198–205.
A.T. Ali, Position vectors of slant helices in Euclidean 3-space, J. Egyptian Math. Soc. 20, (2012), 1–6.
M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997), 1503–1509.
C. Boyer, History of Mathematics, Wiley, New york, 1968.
C. Camci, K. Ilarslan, L. Kula and H.H. Hacisalihoglu, Harmonic curvatures and generalized helices in En, Chaos, Solitons and Fractals 40 (2009), 2590–2596.
L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn and Co., 1909.
H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73 (1996), 699–704.
H.H. Hacisalihoglu, Differential Geometry, Ankara University, Faculty of Science Press, 2000. [14] S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004), 531–537.
W. Kuhnel, Differential Geometry: Curves - Surfaces - Manifolds, Wiesdaden: Braunchweig; 1999. [16] L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comp. 169 (2005), 600–607.
L. Kula, N. Ekmekci, Y. Yayli and K. Ilarslan, Characterizations of slant helices in Euclidean 3-space, Tur. J. Math. 33 (2009), 1–13.
M.M. Lipschutz, Schum,s Outline of Theory and Problems of Differential Geometry, McGraw-Hill Book Company, New York, 1969.
R.S. Milman and G.D. Parker, Elements of Differential Geometry, Prentice-Hall Inc., Engle- wood Cliffs, New Jersey, 1977.
J. Monterde, Curves with constant curvature ratios, Bulletin of Mexican Mathematic Society, 3a serie vol. 13 (2007), 177–186.
J. Monterde, Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. Design 26 (2009), 271–278.
M. Petrovic-Torgasev and E. Sucurovic, W-curves in Minkowski space-time, Novi Sad J. Math. 32(2) (2002), 55–65.
E. Salkowski, Zur transformation von raumkurven, Mathematische Annalen 66 (1909), 517– 557. [24] P.D. Scofield, Curves of constant precession, Amer. Math. Monthly 102 (1995), 531–537.
D.J. Struik, Lectures in Classical Differential Geometry, Addison,-Wesley, Reading, MA, 1961. [26] M. Turgut and S. Yilmaz, Contributions to classical differential geometry of the curves in E3, Scientia Magna 4 (2008), 5–9.
1- Mathematics Department, Faculty of Science, Minia University, Minia, Egypt.
2- Al-Azhar University, Faculty of Science, Mathematics Department, Nasr City, 11884, Cairo, Egypt.
3- King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah, 21589, Saudi Arabia.
E-mail address: elsabbaghmostafa@yahoo.com and atali71@yahoo.com
Elsabbagh, M. F., & T.alı, A. (2013). SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS. Konuralp Journal of Mathematics, 1(2), 80-90.
AMA
Elsabbagh MF, T.alı A. SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS. Konuralp J. Math. October 2013;1(2):80-90.
Chicago
Elsabbagh, Mostafa F., and Ahmad T.alı. “SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS”. Konuralp Journal of Mathematics 1, no. 2 (October 2013): 80-90.
EndNote
Elsabbagh MF, T.alı A (October 1, 2013) SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS. Konuralp Journal of Mathematics 1 2 80–90.
IEEE
M. F. Elsabbagh and A. T.alı, “SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS”, Konuralp J. Math., vol. 1, no. 2, pp. 80–90, 2013.
ISNAD
Elsabbagh, Mostafa F. - T.alı, Ahmad. “SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS”. Konuralp Journal of Mathematics 1/2 (October 2013), 80-90.
JAMA
Elsabbagh MF, T.alı A. SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS. Konuralp J. Math. 2013;1:80–90.
MLA
Elsabbagh, Mostafa F. and Ahmad T.alı. “SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS”. Konuralp Journal of Mathematics, vol. 1, no. 2, 2013, pp. 80-90.
Vancouver
Elsabbagh MF, T.alı A. SIMILAR CURVES WITH VARIABLE TRANSFORMATIONS. Konuralp J. Math. 2013;1(2):80-9.