BibTex RIS Kaynak Göster

FRENET FRAMES AND FRENET INVARIANTS OF SPACELIKE RULED SURFACES

Yıl 2017, Cilt: 19 Sayı: 57, 712 - 722, 01.09.2017

Öz

In this study, we introduce the Chasles theorem for spacelike ruled surfaces and give the Frenet frames and invariants of a spacelike ruled surface and of its directing cone. We show that a spacelike ruled surface and its directing cone have the same Frenet frame

Kaynakça

  • Beem, J.K., Ehrlich, P.E. 1981. Global Lorentzian Dekker, New York. Marcel
  • Dillen, F., Sodsiri, W. 2005. Ruled surfaces of Weingarten type in Minkowski 3-space: J. Geom., Vol. 83, No. DOI:10.1007/s00022-005-0002-4
  • Ekici, C., Özüsağlam, E. 2012. On the Method of Determination of a Developable Timelike Ruled Surface: KJSE- Kuwait Journal of Science & Engineering, Vol. 39(1A), pp. 19-41.
  • Ekici, C., Öztürk, H. 2013. On Timelike Ruled Surfaces in Minkowski 3- Space: Universal Journal of Applied Science, Vol. 1, No. 2, pp. 56-63. DOI: 10.13189/ujas.2013.010205
  • Greub, W. 1975. Linear Algebra, Fourth ed., Springer-Verlag, New York.
  • Guggenheimer, H. 1963. Differential Geometry, McGraw- Hill Book Comp. Inc. London, Lib. Cong. Cat. Card No. 68-12118.
  • Karger, A. Novak, J. 1978. Space Kinematics and Lie Groups. STNL Publishers of Technical Lit., Prague, Czechoslovakia.
  • Kim, Y.H., Yoon, W.D. 2004. Classification of ruled surfaces in Minkowski 3-space: Journal of Geometry and Physics, Vol. 49(1), pp. 89-100. 0440(03)00084-6.
  • Küçük, A. 2004. On the developable timelike trajectory ruled surfaces in Lorentz 3-space IR: App. Math. Comput., Vol. 157(2), pp. 483-489. DOI: 10.1016/j.amc.2003.09.001.
  • O’Neill, B. 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, London.
  • Önder, M., Uğurlu, H.H. 2013. Frenet Frames and Invariants of Timelike Ruled Surfaces: Ain Shams Eng J., Vol. 4, pp. 507-513. DOI: 10.1016/j.asej.2012.10.003.
  • Peternel, M., Pottmann, H., Ravani, B. 1999. geometry of ruled surfaces: Comp. Aided Geom. Design, Vol. 31, pp. 17- 32. 4485(98)00077-3.
  • Ratcliffe, J.G. 2006. Foundations of Hyperbolic Manifolds, Springer.
  • Ravani, B., Ku, T.S. 1991. Bertrand Offsets of ruled and developable surfaces: Comp. Aided Geom. Design, Vol. 23, No. 2, pp. 147-152. DOI: 10.1016/0010-4485(91)90005-H
  • Turgut, A,, Hacısalihoğlu, H.H. 1997. Timelike ruled surfaces in the Minkowski 3-space: Far East J. Math. Sci., Vol. 5, No. 1, pp. 83-90.
  • Uğurlu, H.H., Çalışkan, A. 2012. Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Celal Bayar Üniversitesi Yayınları, Yayın No: 0006.
  • Wang, D.L., Liu, J., Xiao, D.Z. 1997. Kinematic Differential Geometry of a Rigid Body in Spatial Motion I-A New Adjoin Approach and Instantaneous Properties of a Point Trajectory in Spatial Kinematics: Mech. and Mach. Theory, Vol. 32, No. 4, pp. 419-432. DOI: 114X(96)00075-4
  • Wang, D.L., Liu, J., Xiao, D.Z. 1997. Kinematic Differential Geometry of a Rigid Body in Spatial Motion II-A New Instantaneous Properties of a Line Trajectory in Spatial Kinematics: Mech. and Mach. Theory, Vol. 32, No. 4, pp. 433-444. DOI: 10.1016/S0094- 114X(96)00076-6. and
  • Motion: Mech. and Mach. Theory, Vol. , No. 4, pp. 445-457. DOI: 1016/S0094-114X(96)00077-8.

SPACELİKE REGLE YÜZEYLERİN FRENET ÇATILARI VE FRENET İNVARYANTLARI

Yıl 2017, Cilt: 19 Sayı: 57, 712 - 722, 01.09.2017

Öz

1Bağımsız Araştırmacı, Delibekirli Mahallesi, Tepe Sokak, No: 63, 31440, Kırıkhan, Hatay 2Gazi Üniversitesi, Gazi Eğitim Fakültesi, Orta Öğretim Fen ve Matematik Alanları Eğitimi Bölümü, 06500, Ankara

Kaynakça

  • Beem, J.K., Ehrlich, P.E. 1981. Global Lorentzian Dekker, New York. Marcel
  • Dillen, F., Sodsiri, W. 2005. Ruled surfaces of Weingarten type in Minkowski 3-space: J. Geom., Vol. 83, No. DOI:10.1007/s00022-005-0002-4
  • Ekici, C., Özüsağlam, E. 2012. On the Method of Determination of a Developable Timelike Ruled Surface: KJSE- Kuwait Journal of Science & Engineering, Vol. 39(1A), pp. 19-41.
  • Ekici, C., Öztürk, H. 2013. On Timelike Ruled Surfaces in Minkowski 3- Space: Universal Journal of Applied Science, Vol. 1, No. 2, pp. 56-63. DOI: 10.13189/ujas.2013.010205
  • Greub, W. 1975. Linear Algebra, Fourth ed., Springer-Verlag, New York.
  • Guggenheimer, H. 1963. Differential Geometry, McGraw- Hill Book Comp. Inc. London, Lib. Cong. Cat. Card No. 68-12118.
  • Karger, A. Novak, J. 1978. Space Kinematics and Lie Groups. STNL Publishers of Technical Lit., Prague, Czechoslovakia.
  • Kim, Y.H., Yoon, W.D. 2004. Classification of ruled surfaces in Minkowski 3-space: Journal of Geometry and Physics, Vol. 49(1), pp. 89-100. 0440(03)00084-6.
  • Küçük, A. 2004. On the developable timelike trajectory ruled surfaces in Lorentz 3-space IR: App. Math. Comput., Vol. 157(2), pp. 483-489. DOI: 10.1016/j.amc.2003.09.001.
  • O’Neill, B. 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, London.
  • Önder, M., Uğurlu, H.H. 2013. Frenet Frames and Invariants of Timelike Ruled Surfaces: Ain Shams Eng J., Vol. 4, pp. 507-513. DOI: 10.1016/j.asej.2012.10.003.
  • Peternel, M., Pottmann, H., Ravani, B. 1999. geometry of ruled surfaces: Comp. Aided Geom. Design, Vol. 31, pp. 17- 32. 4485(98)00077-3.
  • Ratcliffe, J.G. 2006. Foundations of Hyperbolic Manifolds, Springer.
  • Ravani, B., Ku, T.S. 1991. Bertrand Offsets of ruled and developable surfaces: Comp. Aided Geom. Design, Vol. 23, No. 2, pp. 147-152. DOI: 10.1016/0010-4485(91)90005-H
  • Turgut, A,, Hacısalihoğlu, H.H. 1997. Timelike ruled surfaces in the Minkowski 3-space: Far East J. Math. Sci., Vol. 5, No. 1, pp. 83-90.
  • Uğurlu, H.H., Çalışkan, A. 2012. Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Celal Bayar Üniversitesi Yayınları, Yayın No: 0006.
  • Wang, D.L., Liu, J., Xiao, D.Z. 1997. Kinematic Differential Geometry of a Rigid Body in Spatial Motion I-A New Adjoin Approach and Instantaneous Properties of a Point Trajectory in Spatial Kinematics: Mech. and Mach. Theory, Vol. 32, No. 4, pp. 419-432. DOI: 114X(96)00075-4
  • Wang, D.L., Liu, J., Xiao, D.Z. 1997. Kinematic Differential Geometry of a Rigid Body in Spatial Motion II-A New Instantaneous Properties of a Line Trajectory in Spatial Kinematics: Mech. and Mach. Theory, Vol. 32, No. 4, pp. 433-444. DOI: 10.1016/S0094- 114X(96)00076-6. and
  • Motion: Mech. and Mach. Theory, Vol. , No. 4, pp. 445-457. DOI: 1016/S0094-114X(96)00077-8.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA68TD72HZ
Yazarlar

Mehmet Önder Bu kişi benim

Hasan Hüseyin Uğurlu Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 19 Sayı: 57

Kaynak Göster

Vancouver Önder M, Uğurlu HH. SPACELİKE REGLE YÜZEYLERİN FRENET ÇATILARI VE FRENET İNVARYANTLARI. DEUFMD. 2017;19(57):712-2.

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