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.
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.
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.
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.