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Affine Translation Surfaces in the Isotropic 3-Space

Year 2017, Volume: 10 Issue: 1, 21 - 30, 30.04.2017

Abstract


References

  • [1] Aydin, M. and Mihai, I., On certain surfaces in the isotropic 4-space. Math. Commun. 22 (2017), no.1, 41-51.
  • [2] Aydin, M. and Ogrenmis, O., Homothetical and translation hypersurfaces with constant curvature in the isotropic space. BSG Proceedings 23 (2016), 1-10.
  • [3] Aydin, M., A generalization of translation surfaces with constant curvature in the isotropic space. J. Geom. 107 (2016), no.3, 603-615.
  • [4] Baba-Hamed, Ch., Bekkar, M. and Zoubir, H., Translation surfaces in the three-dimensional Lorentz-Minkowski space satisfying 4ri = iri. Int. J. Math. Anal. 4 (2010), no. 17, 797 - 808.
  • [5] Bekkar, M. and Senoussi, B., Translation surfaces in the 3-dimensional space satisfying 4II ri = iri. J. Geom. 103 (2012), no.3, 367-374.
  • [6] Bukcu, B., Yoon, D.W. and Karacan, M.K., Translation surfaces in the 3-dimensional simply isotropic space I13 satisfying 4IIIxi = ixi. Konuralp J. Math. 4 (2016), no. 1, 275-281.
  • [7] Cetin, M., Tuncer, Y. and Ekmekci, N., Translation surfaces in Euclidean 3-space. Int. J. Phys. Math. Sci. 2 (2011), 49-56.
  • [8] Chen, B.-Y., On submanifolds of finite type. Soochow J. Math. 9 (1983), 65-81.
  • [9] Chen, B.-Y., Total mean curvature and submanifolds of finite type. World Scientific. Singapor-New Jersey-London, 1984.
  • [10] Chen, B.-Y., Decu S. and Verstraelen, L., Notes on isotropic geometry of production models. Kragujevac J. Math. 38 (2014), no. 1, 23-33.
  • [11] Chen, B.-Y., Some open problems and conjectures on submanifolds of finite type: recent development. Tamkang. J. Math. 45 (2014), no.1, 87-108.
  • [12] Dillen, F., Verstraelen, L. and Zafindratafa, G., A generalization of the translation surfaces of Scherk. Differential Geometry in Honor of Radu Rosca: Meeting on Pure and Applied Differential Geometry, Leuven, Belgium, 1989, KU Leuven, Departement Wiskunde (1991), pp. 107–109.
  • [13] Karacan, M.K., Yoon, D.W. and Bukcu, B., Translation surfaces in the three dimensional simply isotropic space I13 . Int. J. Geom. Methods Mod. Phys. 13, 1650088 (2016) (9 pages) DOI: http://dx.doi.org/10.1142/S0219887816500882.
  • [14] Liu, H., Translation surfaces with constant mean curvature in 3-dimensional spaces. J. Geom. 64 (1999), no. 1-2, 141–149.
  • [15] Liu, H. and Yu, Y., Affine translation surfaces in Euclidean 3-space. In: Proceedings of the Japan Academy, Ser. A, Mathematical Sciences 89 Ser. A (2013), 111–113.
  • [16] Liu, H., Jung, S.D., Affine translation surfaces with constant mean curvature in Euclidean 3-space. J. Geom. DOI 10.1007/s00022-016-0348- 9, in press.
  • [17] Lopez, R. and Moruz, M., Translation and homothetical surfaces in Euclidean space with constant curvature. J. Korean Math. Soc. 52 (2015), no. 3, 523-535.
  • [18] Milin-Sipus, Z. and Divjak, B., Mappings of ruled surfaces in simply isotropic space I13 that preserve the generators. Monatsh. Math. 139 (2003), 235–245.
  • [19] Milin-Sipus, Z., Translation surfaces of constant curvatures in a simply isotropic space. Period. Math. Hung. 68 (2014), 160–175.
  • [20] Moruz, M. and Munteanu, M.I., Minimal translation hypersurfaces in E4: J. Math. Anal. Appl. 439 (2016), no. 2, 798-812.
  • [21] Munteanu, M.I., Palmas, O. and Ruiz-Hernandez, G., Minimal translation hypersurfaces in Euclidean spaces. Mediterranean. J. Math. 13 (2016), 2659-2676.
  • [22] Ogrenmis, A.O., Rotational surfaces in isotropic spaces satisfying Weingarten conditions. Open Physics 14 (2016), no. 9, 221–225.
  • [23] Pottmann, H., Grohs, P. and Mitra, N.J., Laguerre minimal surfaces, isotropic geometry and linear elasticity. Adv. Comput. Math. 31 (2009), 391-419.
  • [24] Sachs, H., Isotrope geometrie des raumes. Vieweg Verlag, Braunschweig, 1990.
  • [25] Seo, K., Translation hypersurfaces with constant curvature in space forms. Osaka J. Math. 50 (2013), 631-641.
  • [26] Scherk, H.F., Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen. J. Reine Angew. Math. 13 (1835), 185-208.
  • [27] Strubecker, K., Über die isotropoen Gegenstücke der Minimalfläche von Scherk. J. Reine Angew. Math. 293 (1977), 22–51.
  • [28] Sun, H., On affine translation surfaces of constant mean curvature. Kumamoto J. Math. 13 (2000), 49-57.
  • [29] Verstraelen, L., Walrave, J. and Yaprak, S., The minimal translation surfaces in Euclidean space. Soochow J. Math. 20 (1994), 77-82.
  • [30] Yang, D. and Fu, Y., On affine translation surfaces in affine space. J. Math. Anal. Appl. 440 (2016), no. 2, 437-450.
Year 2017, Volume: 10 Issue: 1, 21 - 30, 30.04.2017

Abstract

References

  • [1] Aydin, M. and Mihai, I., On certain surfaces in the isotropic 4-space. Math. Commun. 22 (2017), no.1, 41-51.
  • [2] Aydin, M. and Ogrenmis, O., Homothetical and translation hypersurfaces with constant curvature in the isotropic space. BSG Proceedings 23 (2016), 1-10.
  • [3] Aydin, M., A generalization of translation surfaces with constant curvature in the isotropic space. J. Geom. 107 (2016), no.3, 603-615.
  • [4] Baba-Hamed, Ch., Bekkar, M. and Zoubir, H., Translation surfaces in the three-dimensional Lorentz-Minkowski space satisfying 4ri = iri. Int. J. Math. Anal. 4 (2010), no. 17, 797 - 808.
  • [5] Bekkar, M. and Senoussi, B., Translation surfaces in the 3-dimensional space satisfying 4II ri = iri. J. Geom. 103 (2012), no.3, 367-374.
  • [6] Bukcu, B., Yoon, D.W. and Karacan, M.K., Translation surfaces in the 3-dimensional simply isotropic space I13 satisfying 4IIIxi = ixi. Konuralp J. Math. 4 (2016), no. 1, 275-281.
  • [7] Cetin, M., Tuncer, Y. and Ekmekci, N., Translation surfaces in Euclidean 3-space. Int. J. Phys. Math. Sci. 2 (2011), 49-56.
  • [8] Chen, B.-Y., On submanifolds of finite type. Soochow J. Math. 9 (1983), 65-81.
  • [9] Chen, B.-Y., Total mean curvature and submanifolds of finite type. World Scientific. Singapor-New Jersey-London, 1984.
  • [10] Chen, B.-Y., Decu S. and Verstraelen, L., Notes on isotropic geometry of production models. Kragujevac J. Math. 38 (2014), no. 1, 23-33.
  • [11] Chen, B.-Y., Some open problems and conjectures on submanifolds of finite type: recent development. Tamkang. J. Math. 45 (2014), no.1, 87-108.
  • [12] Dillen, F., Verstraelen, L. and Zafindratafa, G., A generalization of the translation surfaces of Scherk. Differential Geometry in Honor of Radu Rosca: Meeting on Pure and Applied Differential Geometry, Leuven, Belgium, 1989, KU Leuven, Departement Wiskunde (1991), pp. 107–109.
  • [13] Karacan, M.K., Yoon, D.W. and Bukcu, B., Translation surfaces in the three dimensional simply isotropic space I13 . Int. J. Geom. Methods Mod. Phys. 13, 1650088 (2016) (9 pages) DOI: http://dx.doi.org/10.1142/S0219887816500882.
  • [14] Liu, H., Translation surfaces with constant mean curvature in 3-dimensional spaces. J. Geom. 64 (1999), no. 1-2, 141–149.
  • [15] Liu, H. and Yu, Y., Affine translation surfaces in Euclidean 3-space. In: Proceedings of the Japan Academy, Ser. A, Mathematical Sciences 89 Ser. A (2013), 111–113.
  • [16] Liu, H., Jung, S.D., Affine translation surfaces with constant mean curvature in Euclidean 3-space. J. Geom. DOI 10.1007/s00022-016-0348- 9, in press.
  • [17] Lopez, R. and Moruz, M., Translation and homothetical surfaces in Euclidean space with constant curvature. J. Korean Math. Soc. 52 (2015), no. 3, 523-535.
  • [18] Milin-Sipus, Z. and Divjak, B., Mappings of ruled surfaces in simply isotropic space I13 that preserve the generators. Monatsh. Math. 139 (2003), 235–245.
  • [19] Milin-Sipus, Z., Translation surfaces of constant curvatures in a simply isotropic space. Period. Math. Hung. 68 (2014), 160–175.
  • [20] Moruz, M. and Munteanu, M.I., Minimal translation hypersurfaces in E4: J. Math. Anal. Appl. 439 (2016), no. 2, 798-812.
  • [21] Munteanu, M.I., Palmas, O. and Ruiz-Hernandez, G., Minimal translation hypersurfaces in Euclidean spaces. Mediterranean. J. Math. 13 (2016), 2659-2676.
  • [22] Ogrenmis, A.O., Rotational surfaces in isotropic spaces satisfying Weingarten conditions. Open Physics 14 (2016), no. 9, 221–225.
  • [23] Pottmann, H., Grohs, P. and Mitra, N.J., Laguerre minimal surfaces, isotropic geometry and linear elasticity. Adv. Comput. Math. 31 (2009), 391-419.
  • [24] Sachs, H., Isotrope geometrie des raumes. Vieweg Verlag, Braunschweig, 1990.
  • [25] Seo, K., Translation hypersurfaces with constant curvature in space forms. Osaka J. Math. 50 (2013), 631-641.
  • [26] Scherk, H.F., Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen. J. Reine Angew. Math. 13 (1835), 185-208.
  • [27] Strubecker, K., Über die isotropoen Gegenstücke der Minimalfläche von Scherk. J. Reine Angew. Math. 293 (1977), 22–51.
  • [28] Sun, H., On affine translation surfaces of constant mean curvature. Kumamoto J. Math. 13 (2000), 49-57.
  • [29] Verstraelen, L., Walrave, J. and Yaprak, S., The minimal translation surfaces in Euclidean space. Soochow J. Math. 20 (1994), 77-82.
  • [30] Yang, D. and Fu, Y., On affine translation surfaces in affine space. J. Math. Anal. Appl. 440 (2016), no. 2, 437-450.
There are 30 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Muhittin Evren Aydin This is me

Mahmut Ergüt This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Aydin, M. E., & Ergüt, M. (2017). Affine Translation Surfaces in the Isotropic 3-Space. International Electronic Journal of Geometry, 10(1), 21-30.
AMA Aydin ME, Ergüt M. Affine Translation Surfaces in the Isotropic 3-Space. Int. Electron. J. Geom. April 2017;10(1):21-30.
Chicago Aydin, Muhittin Evren, and Mahmut Ergüt. “Affine Translation Surfaces in the Isotropic 3-Space”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 21-30.
EndNote Aydin ME, Ergüt M (April 1, 2017) Affine Translation Surfaces in the Isotropic 3-Space. International Electronic Journal of Geometry 10 1 21–30.
IEEE M. E. Aydin and M. Ergüt, “Affine Translation Surfaces in the Isotropic 3-Space”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 21–30, 2017.
ISNAD Aydin, Muhittin Evren - Ergüt, Mahmut. “Affine Translation Surfaces in the Isotropic 3-Space”. International Electronic Journal of Geometry 10/1 (April 2017), 21-30.
JAMA Aydin ME, Ergüt M. Affine Translation Surfaces in the Isotropic 3-Space. Int. Electron. J. Geom. 2017;10:21–30.
MLA Aydin, Muhittin Evren and Mahmut Ergüt. “Affine Translation Surfaces in the Isotropic 3-Space”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 21-30.
Vancouver Aydin ME, Ergüt M. Affine Translation Surfaces in the Isotropic 3-Space. Int. Electron. J. Geom. 2017;10(1):21-30.