Affine Translation Surfaces in the Isotropic 3-Space

Yıl 2017, Cilt: 10 Sayı: 1, 21 - 30, 30.04.2017

Muhittin Evren Aydin Mahmut Ergüt

Öz

Anahtar Kelimeler

Isotropic space, affine translation surface, Weingarten surface

Kaynakça

• [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.