BibTex RIS Kaynak Göster

ON PARALLEL SURFACES IN MINKOWSKI 3-SPACE

Yıl 2013, Cilt: 3 Sayı: 2, 214 - 222, 01.12.2013

Öz

In this paper, we study on some properties of parallel surfaces in Minkowski 3-space. The results given in this paper were given in Euclidean space by [7, 8]. By using these two former studies, we show these properties in Minkowski 3-space. Also we give the relation among the fundamental forms of parallel surfaces in Minkowski 3-space. Finally we show that how a curve which is geodesic on M become again a geodesic on parallel surface Mr by the normal map in Minkowski 3-space.

Kaynakça

  • [1] C¸ ¨oken, A. C¸., C¸iftci, U. and Ekici, C., 2008, On parallel timelike ruled surfaces with timelike rulings, ¨ Kuwait Journal of Science & Engineering, 35, 21–31.
  • [2] Craig, T., Note on parallel surfaces, Journal f¨ur die Reine und Angewandte Mathematik (Crelle’s journal), 94, 162–170., 1883.
  • [3] Eisenhart, L.P., 1909, A treatise on the differential geometry of curves and surfaces, Ginn and Company, Boston: New York.
  • [4] G¨org¨ul¨u, A. and C¸ ¨oken, C., The dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in semi-Euclidean space R n 1 . Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994.
  • [5] A. G¨org¨ul¨u and A. C. C¸ ¨oken, The Euler theorem for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space E n+1 1 , Journ. Inst. Math. and Comp. Sci. (Math. Series) Vol:6, No.2 (1993), 161-165.
  • [6] Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993.
  • [7] Hacısaliho˘glu, H. H., 2000, Diferensiyel geometri, Cilt I-II, Ankara Universitesi, Fen Fak¨ultesi ¨ Yayınları.
  • [8] Hicks, Noel J., Notes on Differential Geometry, Van Nostrant Reinhold Company, London, 1974.
  • [9] K¨uhnel, W., 2002, Differential geometry, curves-surfaces-manifolds, American Mathematical Society.
  • [10] Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, Mini-Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008
  • [11] Nizamoglu, S¸., 1986, Surfaces r´egl´ees parall`eles, Ege Univ. Fen Fak. Derg., 9 (Ser. A), 37-48. ¨ [12] O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983.
  • [13] Patriciu, A. M., 2010, On some 1,3H3-helicoidal surfaces and their parallel surfaces at a certain distance in 3-dimensional Minkowski space, Annals of the University of Craiova, Maths. and Compt.Science Series, V 37 (4), 93-98.
Yıl 2013, Cilt: 3 Sayı: 2, 214 - 222, 01.12.2013

Öz

Kaynakça

  • [1] C¸ ¨oken, A. C¸., C¸iftci, U. and Ekici, C., 2008, On parallel timelike ruled surfaces with timelike rulings, ¨ Kuwait Journal of Science & Engineering, 35, 21–31.
  • [2] Craig, T., Note on parallel surfaces, Journal f¨ur die Reine und Angewandte Mathematik (Crelle’s journal), 94, 162–170., 1883.
  • [3] Eisenhart, L.P., 1909, A treatise on the differential geometry of curves and surfaces, Ginn and Company, Boston: New York.
  • [4] G¨org¨ul¨u, A. and C¸ ¨oken, C., The dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in semi-Euclidean space R n 1 . Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994.
  • [5] A. G¨org¨ul¨u and A. C. C¸ ¨oken, The Euler theorem for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space E n+1 1 , Journ. Inst. Math. and Comp. Sci. (Math. Series) Vol:6, No.2 (1993), 161-165.
  • [6] Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993.
  • [7] Hacısaliho˘glu, H. H., 2000, Diferensiyel geometri, Cilt I-II, Ankara Universitesi, Fen Fak¨ultesi ¨ Yayınları.
  • [8] Hicks, Noel J., Notes on Differential Geometry, Van Nostrant Reinhold Company, London, 1974.
  • [9] K¨uhnel, W., 2002, Differential geometry, curves-surfaces-manifolds, American Mathematical Society.
  • [10] Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, Mini-Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008
  • [11] Nizamoglu, S¸., 1986, Surfaces r´egl´ees parall`eles, Ege Univ. Fen Fak. Derg., 9 (Ser. A), 37-48. ¨ [12] O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983.
  • [13] Patriciu, A. M., 2010, On some 1,3H3-helicoidal surfaces and their parallel surfaces at a certain distance in 3-dimensional Minkowski space, Annals of the University of Craiova, Maths. and Compt.Science Series, V 37 (4), 93-98.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Yasin Unluturk Bu kişi benim

Erdal Ozusaglam Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 3 Sayı: 2

Kaynak Göster