Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 1, 461 - 472, 30.06.2020
https://doi.org/10.31801/cfsuasmas.544204

Öz

Kaynakça

  • Andrade, M. Calculus of Affine Structures and Applications for Isosurfaces (in Portuguese), PhD dissertation, Rio de Janeiro, August 2011.
  • Andrade, M. and Lewiner, T. Affine-invariant Curvature Estimators for Implicit Surfaces, Computer Aided Geometric Design 29 (2012),162--173.
  • Arslan, K., Bayram, B., Bulca, B. and Ozturk, G. On translation surfaces in 4-dimensional Euclidean space, Acta Et Commentationes Universitatis Tartuensis De Mathematica, 20(2) (2016),123-133.
  • Blaschke, W. Vorlesungen über Differentialgeometrie II, Springer, Berlin, 1923.L. Verstraelen, L. Vrancken, Affine variation formulas and affine minimal surfaces, Michigan Math. J., 36 (1989), 77--93.
  • Bulca, B. On generalized LN-Surfaces in E⁴, Mathematical Sciences And Applications E-Notes, 1(2) (2013), 35-41 .
  • Goemans, W. Surfaces in three-dimensional Euclidean and Minkowski space, in particular a study of Weingarten surfaces, PhD. Dissertation, September 2010.
  • Huamani, E. F. C. Affine Minimal Surfaces with Singularities, Masters dissertation,Rio de Janeiro,September 2017.
  • Fu, Y. and Hou, Z.H. Affine Translation Surfaces with Constant Gauss Curvatures, Kyungpook Math. J., 50 (2010), 337-343.
  • Juttler, B. and Sampoli, M.L. Hermite interpolation by piecewise polynomial surfaces with rational offsets, Comp. Aided Geom. Design, 17 (2000), 361-385.
  • Magid, M. and Vrancken, L. Affine Translation Surfaces, Results Math., 35 (1999),134-144.
  • Manhart, F. Die Affin minimal rückungsflächen, Arch. Math., 44 (1985), 547-556.
  • Liu, H.L. Translation Surfaces with Constant Mean Curvature in 3-dimensional spaces, J.Geom., 64 (1999), 141-149.
  • Sampoli, M.L. Computing the convolution and the Minkowski sum of surfaces, Proceedings of the 21st Spring Conference on Computer Graphics, Budmerice,Slovakia, May 12-14, (2005),111-117
  • Sampoli, M. L., Peternell, M. and Jüttler, B. Rational surfaces with linear normals and their convolutions with rational surfaces, Comp. Aided Geom. Design, 23 (2006), 179-192 Sun, H. On affine translation surfaces of constant mean curvature, Kumamoto J. Math., 13 (2000) 49---57.
  • Yang, Y., Yu, Y.H. and Liu, H.L. Linear Weingarten centroaffine translation surfaces in R³, J. Math. Anal. Appl., 375 (2011), 458-466.
  • Yanga, D.Fu, Y.,On affine translation surfaces in affine space, J. Math. Anal. Appl., 440 (2016), 437-450. Yoon, D.W. Some Classification of Translation surfaces in Galilean 3-space, Int. Journal of Math. Analysis, 6(28) (2012), 1355-1361.

LCN-translation surfaces in affine 3-space

Yıl 2020, Cilt: 69 Sayı: 1, 461 - 472, 30.06.2020
https://doi.org/10.31801/cfsuasmas.544204

Öz

In this paper, we give the classification of the LCN-translation surfaces
with zero mean curvature and zero Gaussian curvature in 3-dimensional
Affine space.

Kaynakça

  • Andrade, M. Calculus of Affine Structures and Applications for Isosurfaces (in Portuguese), PhD dissertation, Rio de Janeiro, August 2011.
  • Andrade, M. and Lewiner, T. Affine-invariant Curvature Estimators for Implicit Surfaces, Computer Aided Geometric Design 29 (2012),162--173.
  • Arslan, K., Bayram, B., Bulca, B. and Ozturk, G. On translation surfaces in 4-dimensional Euclidean space, Acta Et Commentationes Universitatis Tartuensis De Mathematica, 20(2) (2016),123-133.
  • Blaschke, W. Vorlesungen über Differentialgeometrie II, Springer, Berlin, 1923.L. Verstraelen, L. Vrancken, Affine variation formulas and affine minimal surfaces, Michigan Math. J., 36 (1989), 77--93.
  • Bulca, B. On generalized LN-Surfaces in E⁴, Mathematical Sciences And Applications E-Notes, 1(2) (2013), 35-41 .
  • Goemans, W. Surfaces in three-dimensional Euclidean and Minkowski space, in particular a study of Weingarten surfaces, PhD. Dissertation, September 2010.
  • Huamani, E. F. C. Affine Minimal Surfaces with Singularities, Masters dissertation,Rio de Janeiro,September 2017.
  • Fu, Y. and Hou, Z.H. Affine Translation Surfaces with Constant Gauss Curvatures, Kyungpook Math. J., 50 (2010), 337-343.
  • Juttler, B. and Sampoli, M.L. Hermite interpolation by piecewise polynomial surfaces with rational offsets, Comp. Aided Geom. Design, 17 (2000), 361-385.
  • Magid, M. and Vrancken, L. Affine Translation Surfaces, Results Math., 35 (1999),134-144.
  • Manhart, F. Die Affin minimal rückungsflächen, Arch. Math., 44 (1985), 547-556.
  • Liu, H.L. Translation Surfaces with Constant Mean Curvature in 3-dimensional spaces, J.Geom., 64 (1999), 141-149.
  • Sampoli, M.L. Computing the convolution and the Minkowski sum of surfaces, Proceedings of the 21st Spring Conference on Computer Graphics, Budmerice,Slovakia, May 12-14, (2005),111-117
  • Sampoli, M. L., Peternell, M. and Jüttler, B. Rational surfaces with linear normals and their convolutions with rational surfaces, Comp. Aided Geom. Design, 23 (2006), 179-192 Sun, H. On affine translation surfaces of constant mean curvature, Kumamoto J. Math., 13 (2000) 49---57.
  • Yang, Y., Yu, Y.H. and Liu, H.L. Linear Weingarten centroaffine translation surfaces in R³, J. Math. Anal. Appl., 375 (2011), 458-466.
  • Yanga, D.Fu, Y.,On affine translation surfaces in affine space, J. Math. Anal. Appl., 440 (2016), 437-450. Yoon, D.W. Some Classification of Translation surfaces in Galilean 3-space, Int. Journal of Math. Analysis, 6(28) (2012), 1355-1361.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Murat Kemal Karacan 0000-0002-2832-9444

Nural Yüksel 0000-0003-3360-5148

Yılmaz Tunçer 0000-0002-2398-866X

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 25 Mart 2019
Kabul Tarihi 19 Kasım 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Karacan, M. K., Yüksel, N., & Tunçer, Y. (2020). LCN-translation surfaces in affine 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 461-472. https://doi.org/10.31801/cfsuasmas.544204
AMA Karacan MK, Yüksel N, Tunçer Y. LCN-translation surfaces in affine 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):461-472. doi:10.31801/cfsuasmas.544204
Chicago Karacan, Murat Kemal, Nural Yüksel, ve Yılmaz Tunçer. “LCN-Translation Surfaces in Affine 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 461-72. https://doi.org/10.31801/cfsuasmas.544204.
EndNote Karacan MK, Yüksel N, Tunçer Y (01 Haziran 2020) LCN-translation surfaces in affine 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 461–472.
IEEE M. K. Karacan, N. Yüksel, ve Y. Tunçer, “LCN-translation surfaces in affine 3-space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 461–472, 2020, doi: 10.31801/cfsuasmas.544204.
ISNAD Karacan, Murat Kemal vd. “LCN-Translation Surfaces in Affine 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 461-472. https://doi.org/10.31801/cfsuasmas.544204.
JAMA Karacan MK, Yüksel N, Tunçer Y. LCN-translation surfaces in affine 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:461–472.
MLA Karacan, Murat Kemal vd. “LCN-Translation Surfaces in Affine 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 461-72, doi:10.31801/cfsuasmas.544204.
Vancouver Karacan MK, Yüksel N, Tunçer Y. LCN-translation surfaces in affine 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):461-72.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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