BibTex RIS Kaynak Göster

Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space

Yıl 2013, Cilt: 1 Sayı: 1, 85 - 92, 01.04.2013

Öz

In this work, it is shown that parallel surfaces of spacelike ruled surfaces which are developable are spacelike ruled Weingarten surfaces. It is also shown that parallel surfaces of non-developable ruled Weingarten surfaces are again Weingarten surfaces. Finally, some properties of that kind parallel surfaces are obtained in Minkowski 3-space

Kaynakça

  • Beltrami, E., Risoluzione di un problema relativo alla teoria delle supercie gobbe, Ann. Mat. Pura Appl., 7, 139-150., 1865.
  • Brunt, B., Weingarten surfaces design and application of curves and surfaces, Fisher, R., (Ed.), Mathematics of surfaces V, Oxford Univ. Press., 1994.
  • Brunt, B. and Grant, K., Potential applications of Weingarten surfaces in CAGD. I: Weingarten surfaces and surface shape investigation, Comput. Aided Geom. Des., 13, 569-582., 1996.
  • Dillen, F. and Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320., 1999.
  • Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom., 83, 10-21., 2005.
  • Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space-II, J. Geom., 84, 37-44., 2005.
  • Dini, U., Sulle super.cie gobbe nelle quali uno dei due raggidi curvatura principale e una funzione dellaltro, Ann. Mat. Pura Appl., 7, 205-210.,1865.
  • Görgülü, A. and Çöken, C., The Dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in
  • Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994.
  • semi-Euclidean space
  • Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993.
  • Hou, Z. H. and Ji, F., Helicoidal surfaces with
  • Kim, M. H. and Yoon, D. W., Weingarten quadric surfaces in a Euclidean 3-space, Turk. J. Math. 34, 1-7., 2010.
  • Koch, R., Die Weingarten-regelflächen, J. Geom. 47, 77-85., 1993.
  • Kühnel, W., Ruled W-surfaces, Arch. Math. (Basel), 62, 475-480., 1994.
  • Lopez, R., Di¤erential 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.
  • O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983.
  • Turgut, A. and Hacısalihoğlu, H. H., Spacelike ruled surfaces in the Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Series A1, v. 46, pp. 83-91, 1997.
  • Unluturk, Y., and Ekici, C., On spacelike parallel ruled surfaces in Minkowski 3-space, (Preprint).
  • Unluturk, Y., Ekici, C., and Özüsağlam, E., On parallel surfaces in Minkowski 3-space, (Preprint).
  • Weingarten, J., Über eine klasse auf einander abwickelbarer .ächen, J. Reine Angew. Math. 59, 382-393, 1861.
  • Weingarten, J., Über eine flächen, derer normalen eine gegebene flächeberühren, Journal für die Reine und Angewandte Mathematik, 62, 61-63, 1863.
  • D. W. Yoon, Some properties of parallel surfaces in Euclidean 3-spaces, Honam Mathematical J. 30, No. 4, pp, 637-644, 2008.

Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in

Yıl 2013, Cilt: 1 Sayı: 1, 85 - 92, 01.04.2013

Öz

Kaynakça

  • Beltrami, E., Risoluzione di un problema relativo alla teoria delle supercie gobbe, Ann. Mat. Pura Appl., 7, 139-150., 1865.
  • Brunt, B., Weingarten surfaces design and application of curves and surfaces, Fisher, R., (Ed.), Mathematics of surfaces V, Oxford Univ. Press., 1994.
  • Brunt, B. and Grant, K., Potential applications of Weingarten surfaces in CAGD. I: Weingarten surfaces and surface shape investigation, Comput. Aided Geom. Des., 13, 569-582., 1996.
  • Dillen, F. and Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320., 1999.
  • Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom., 83, 10-21., 2005.
  • Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space-II, J. Geom., 84, 37-44., 2005.
  • Dini, U., Sulle super.cie gobbe nelle quali uno dei due raggidi curvatura principale e una funzione dellaltro, Ann. Mat. Pura Appl., 7, 205-210.,1865.
  • Görgülü, A. and Çöken, C., The Dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in
  • Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994.
  • semi-Euclidean space
  • Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993.
  • Hou, Z. H. and Ji, F., Helicoidal surfaces with
  • Kim, M. H. and Yoon, D. W., Weingarten quadric surfaces in a Euclidean 3-space, Turk. J. Math. 34, 1-7., 2010.
  • Koch, R., Die Weingarten-regelflächen, J. Geom. 47, 77-85., 1993.
  • Kühnel, W., Ruled W-surfaces, Arch. Math. (Basel), 62, 475-480., 1994.
  • Lopez, R., Di¤erential 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.
  • O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983.
  • Turgut, A. and Hacısalihoğlu, H. H., Spacelike ruled surfaces in the Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Series A1, v. 46, pp. 83-91, 1997.
  • Unluturk, Y., and Ekici, C., On spacelike parallel ruled surfaces in Minkowski 3-space, (Preprint).
  • Unluturk, Y., Ekici, C., and Özüsağlam, E., On parallel surfaces in Minkowski 3-space, (Preprint).
  • Weingarten, J., Über eine klasse auf einander abwickelbarer .ächen, J. Reine Angew. Math. 59, 382-393, 1861.
  • Weingarten, J., Über eine flächen, derer normalen eine gegebene flächeberühren, Journal für die Reine und Angewandte Mathematik, 62, 61-63, 1863.
  • D. W. Yoon, Some properties of parallel surfaces in Euclidean 3-spaces, Honam Mathematical J. 30, No. 4, pp, 637-644, 2008.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Yasin Ünlütürk Bu kişi benim

Cumali Ekici Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 1 Sayı: 1

Kaynak Göster

APA Ünlütürk, Y., & Ekici, C. (2013). Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space. New Trends in Mathematical Sciences, 1(1), 85-92.
AMA Ünlütürk Y, Ekici C. Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space. New Trends in Mathematical Sciences. Nisan 2013;1(1):85-92.
Chicago Ünlütürk, Yasin, ve Cumali Ekici. “Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-Space”. New Trends in Mathematical Sciences 1, sy. 1 (Nisan 2013): 85-92.
EndNote Ünlütürk Y, Ekici C (01 Nisan 2013) Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space. New Trends in Mathematical Sciences 1 1 85–92.
IEEE Y. Ünlütürk ve C. Ekici, “Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space”, New Trends in Mathematical Sciences, c. 1, sy. 1, ss. 85–92, 2013.
ISNAD Ünlütürk, Yasin - Ekici, Cumali. “Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-Space”. New Trends in Mathematical Sciences 1/1 (Nisan 2013), 85-92.
JAMA Ünlütürk Y, Ekici C. Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space. New Trends in Mathematical Sciences. 2013;1:85–92.
MLA Ünlütürk, Yasin ve Cumali Ekici. “Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-Space”. New Trends in Mathematical Sciences, c. 1, sy. 1, 2013, ss. 85-92.
Vancouver Ünlütürk Y, Ekici C. Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space. New Trends in Mathematical Sciences. 2013;1(1):85-92.