Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 12 Sayı: 1, 20 - 25, 27.03.2019

Öz

Kaynakça

  • [1] Baba-Hamed, C. and Bekkar, M., Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying4II ri = iri. J. Geom. 100 (2011), no. 1-2, 1.
  • [2] Baikoussis, C. and Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature. J. Geom. 63 (1998), no. 1, 25-29.
  • [3] Beneki, C.C., Kaimakamis, G. and Papantoniou, B.J., Helicoidal surfaces in three-dimensional Minkowski space. Journal of Mathematical Analysis and Applications, 275 (2002), no. 2, 586-614.
  • [4] Corro, A. V., Pina, R. and Souza, M., Surfaces of rotation with constant extrinsic curvature in a conformally flat 3-space. Results in Mathematics, 60 (2011), no. 1-4, 225.
  • [5] Corwin, I., Hoffman, N., Hurder, S., Šešum, V. and Xu, Y., Differential geometry of manifolds with density. Rose-Hulman Undergrad. Math. J., 7(2006), 1-15.
  • [6] Delaunay, C. H., Sur la surface de révolution dont la courbure moyenne est constante. Journal de mathématiques pures et appliquées (1841), 309-314.
  • [7] Do Carmo, M.P. and Dajczer, M., Helicoidal surfaces with constant mean curvature. Tohoku Mathematical Journal, Second Series 34 (1982), no. 3, 425-435.
  • [8] Hıeu, D.T. and Hoang, N.M., Ruled minimal surfaces in R3 with density ez. Pacific Journal of Mathematics, 243 (2009), no. 2, 277-285.
  • [9] Hou, Z.H. and Ji, F., Helicoidal surfaces with H2 = K in Minkowski 3-space. Journal of mathematical analysis and applications, 325 (2007), no. 1, 101-113.
  • [10] Ji, F. and Hou, Z.H., A kind of helicoidal surfaces in 3-dimensional Minkowski space. Journal of mathematical analysis and applications, 304 (2005), no.2 632-643.
  • [11] Ji, F. and Hou, Z.H., Helicoidal surfaces under the cubic screw motion in Minkowski 3-space. Journal of mathematical analysis and applications, 318 (2006), no. 2, 634-647.
  • [12] Morgan, F., Geometric measure theory: a beginner’s guide. Academic press, 2016.
  • [13] Morgan, F., Manifolds with density. Notices of the AMS, (2005), 853-858.
  • [14] Morgan, F., Myers’ theorem with density. Kodai Mathematical Journal, 29 (2006), no. 3, 455-461.
  • [15] Morgan, F., Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture. American Mathematical Monthly, 116 (2009), no. 2, 134-142.
  • [16] Rafael, L. and Demir, E., Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature. Open Mathematics, 12 (2014), no: 9, 1349-1361.
  • [17] Rayón, P. and Gromov, M., Isoperimetry of waists and concentration of maps. Geometric and functional analysis, 13 (2003), no. 1, 178-215.
  • [18] Rosales, C., Cañete, A., Bayle, V. and Morgan, M., On the isoperimetric problem in Euclidean space with density. Calculus of Variations and Partial Differential Equations, 31 (2008), no. 1, 27-46.
  • [19] Roussos, I.M., The helicoidal surfaces as Bonnet surfaces. Tohoku Mathematical Journal, Second Series 40 (1988), no. 3, 485-490.
  • [20] Yıldız, Ö.G., Hızal, S. and Akyi˘ git, M., Type I+ Helicoidal Surfaces with PrescribedWeighted Mean or Gaussian Curvature in Minkowski Space with Density. Analele Universitatii" Ovidius" Constanta-Seria Matematica, 26 (2018), no. 3, 99-108.
  • [21] Yoon, D.W.,Weighted minimal translation surfaces in Minkowski 3-space with density. International Journal of Geometric Methods in Modern Physics, 14 (2017), no. 12, 1750178.
  • [22] Yoon, D.W., Kim, D.S., Kim, Y.H. and Lee, J.W., Constructions of Helicoidal Surfaces in Euclidean Space with Density. Symmetry 9 (2017), no. 9, 173.

Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity

Yıl 2019, Cilt: 12 Sayı: 1, 20 - 25, 27.03.2019

Öz

In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean
curvature and weighted Gaussian curvature in the Minkowski 3-space R^3_1 with a positive density
function. We get a result for minimal case. Also we give examples of helicoidal surface with
prescribed weighted mean curvature and Gaussian curvature.

Kaynakça

  • [1] Baba-Hamed, C. and Bekkar, M., Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying4II ri = iri. J. Geom. 100 (2011), no. 1-2, 1.
  • [2] Baikoussis, C. and Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature. J. Geom. 63 (1998), no. 1, 25-29.
  • [3] Beneki, C.C., Kaimakamis, G. and Papantoniou, B.J., Helicoidal surfaces in three-dimensional Minkowski space. Journal of Mathematical Analysis and Applications, 275 (2002), no. 2, 586-614.
  • [4] Corro, A. V., Pina, R. and Souza, M., Surfaces of rotation with constant extrinsic curvature in a conformally flat 3-space. Results in Mathematics, 60 (2011), no. 1-4, 225.
  • [5] Corwin, I., Hoffman, N., Hurder, S., Šešum, V. and Xu, Y., Differential geometry of manifolds with density. Rose-Hulman Undergrad. Math. J., 7(2006), 1-15.
  • [6] Delaunay, C. H., Sur la surface de révolution dont la courbure moyenne est constante. Journal de mathématiques pures et appliquées (1841), 309-314.
  • [7] Do Carmo, M.P. and Dajczer, M., Helicoidal surfaces with constant mean curvature. Tohoku Mathematical Journal, Second Series 34 (1982), no. 3, 425-435.
  • [8] Hıeu, D.T. and Hoang, N.M., Ruled minimal surfaces in R3 with density ez. Pacific Journal of Mathematics, 243 (2009), no. 2, 277-285.
  • [9] Hou, Z.H. and Ji, F., Helicoidal surfaces with H2 = K in Minkowski 3-space. Journal of mathematical analysis and applications, 325 (2007), no. 1, 101-113.
  • [10] Ji, F. and Hou, Z.H., A kind of helicoidal surfaces in 3-dimensional Minkowski space. Journal of mathematical analysis and applications, 304 (2005), no.2 632-643.
  • [11] Ji, F. and Hou, Z.H., Helicoidal surfaces under the cubic screw motion in Minkowski 3-space. Journal of mathematical analysis and applications, 318 (2006), no. 2, 634-647.
  • [12] Morgan, F., Geometric measure theory: a beginner’s guide. Academic press, 2016.
  • [13] Morgan, F., Manifolds with density. Notices of the AMS, (2005), 853-858.
  • [14] Morgan, F., Myers’ theorem with density. Kodai Mathematical Journal, 29 (2006), no. 3, 455-461.
  • [15] Morgan, F., Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture. American Mathematical Monthly, 116 (2009), no. 2, 134-142.
  • [16] Rafael, L. and Demir, E., Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature. Open Mathematics, 12 (2014), no: 9, 1349-1361.
  • [17] Rayón, P. and Gromov, M., Isoperimetry of waists and concentration of maps. Geometric and functional analysis, 13 (2003), no. 1, 178-215.
  • [18] Rosales, C., Cañete, A., Bayle, V. and Morgan, M., On the isoperimetric problem in Euclidean space with density. Calculus of Variations and Partial Differential Equations, 31 (2008), no. 1, 27-46.
  • [19] Roussos, I.M., The helicoidal surfaces as Bonnet surfaces. Tohoku Mathematical Journal, Second Series 40 (1988), no. 3, 485-490.
  • [20] Yıldız, Ö.G., Hızal, S. and Akyi˘ git, M., Type I+ Helicoidal Surfaces with PrescribedWeighted Mean or Gaussian Curvature in Minkowski Space with Density. Analele Universitatii" Ovidius" Constanta-Seria Matematica, 26 (2018), no. 3, 99-108.
  • [21] Yoon, D.W.,Weighted minimal translation surfaces in Minkowski 3-space with density. International Journal of Geometric Methods in Modern Physics, 14 (2017), no. 12, 1750178.
  • [22] Yoon, D.W., Kim, D.S., Kim, Y.H. and Lee, J.W., Constructions of Helicoidal Surfaces in Euclidean Space with Density. Symmetry 9 (2017), no. 9, 173.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Önder Gökmen Yıldız

Mahmut Akyiğit

Yayımlanma Tarihi 27 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Yıldız, Ö. G., & Akyiğit, M. (2019). Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. International Electronic Journal of Geometry, 12(1), 20-25.
AMA Yıldız ÖG, Akyiğit M. Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. Int. Electron. J. Geom. Mart 2019;12(1):20-25.
Chicago Yıldız, Önder Gökmen, ve Mahmut Akyiğit. “Constructions of Type III+ Helicoidal Surfaces in Minkowski Space With Desity”. International Electronic Journal of Geometry 12, sy. 1 (Mart 2019): 20-25.
EndNote Yıldız ÖG, Akyiğit M (01 Mart 2019) Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. International Electronic Journal of Geometry 12 1 20–25.
IEEE Ö. G. Yıldız ve M. Akyiğit, “Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity”, Int. Electron. J. Geom., c. 12, sy. 1, ss. 20–25, 2019.
ISNAD Yıldız, Önder Gökmen - Akyiğit, Mahmut. “Constructions of Type III+ Helicoidal Surfaces in Minkowski Space With Desity”. International Electronic Journal of Geometry 12/1 (Mart 2019), 20-25.
JAMA Yıldız ÖG, Akyiğit M. Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. Int. Electron. J. Geom. 2019;12:20–25.
MLA Yıldız, Önder Gökmen ve Mahmut Akyiğit. “Constructions of Type III+ Helicoidal Surfaces in Minkowski Space With Desity”. International Electronic Journal of Geometry, c. 12, sy. 1, 2019, ss. 20-25.
Vancouver Yıldız ÖG, Akyiğit M. Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. Int. Electron. J. Geom. 2019;12(1):20-5.