Research Article
Year 2020,
Volume: 69 Issue: 1, 461 - 472, 30.06.2020
Abstract
References
- 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.
Year 2020,
Volume: 69 Issue: 1, 461 - 472, 30.06.2020
Abstract
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.
References
- 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.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 30, 2020 |
| Submission Date | March 25, 2019 |
| Acceptance Date | November 19, 2019 |
| Published in Issue | Year 2020 Volume: 69 Issue: 1 |
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Cited By
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
