References
- M. E. Aydin and M. Ergut, Isotropic geometry of graph surfaces associated with product production functions in economics, Tamkang J. Math. 47 (2016), no. 4, 433-443.
- M. E. Aydin and A. O. Ogrenmis, Homothetical and translation hypersurfaces with constant curvature in the isotropic space, In: Proceedings of the Balkan Society of Geometers, vol. 23, pp. 1-10, 2015.
- M. E. Aydin and A. O. Ogrenmis, Linear Weingarten factorable surfaces in isotropic spaces, Stud. Univ. Babes-Bolyai Math. 62 (2017), no. 2, 261-268. https://doi.org/10.24193/subbmath.2017.2.11
-
M. Bekkar and B. Senoussi, Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying
${\Delta}r_i={\lambda}_ir_i$ , J. Geom. 103 (2012), no. 1, 17-29. https://doi.org/10.1007/s00022-012-0117-3 - B. Y. Chen, S. Decu, and L. Verstraelen, Notes on isotropic geometry of production models, Kragujevac J. Math. 38 (2014), no. 1, 23-33. https://doi.org/10.5937/KgJMath1401023C
- S. Decu and L. Verstraelen, A note on the isotropical geometry of production surfaces, Kragujevac J. Math. 37 (2013), no. 2, 217-220.
-
F. Dillen, I. Van de Woestyne, L. Verstraelen, and J. T. Walrave, The surface of Scherk in
$E^3$ : A special case in the class of minimal surfaces defined as the sum of two curves, Bull. Inst. Math. Acad. Sin. 26 (1998), no. 4, 257-267. - F. Dillen, W. Goemans, and I. Van de Woestyne, Translation surfaces of Weingarten type in 3-space, Bull. Transilv. Univ. Brasov Ser. III 1(50) (2008), 109-122.
- W. Goemans and I. Van de Woestyne, Translation and homothetical lightlike hypersurfaces of semi-Euclidean space, Kuwait J. Sci. Engrg. 38 (2011), no. 2A, 35-42.
- L. Jiu and H. Sun, On minimal homothetical hypersurfaces, Colloq. Math. 109 (2007), no. 2, 239-249. https://doi.org/10.4064/cm109-2-6
- H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), no. 1-2, 141-149. https://doi.org/10.1007/BF01229219
- R. Lopez, Minimal translation surfaces in hyperbolic space, Beitr. Algebra Geom. 52 (2011), no. 1, 105-112. https://doi.org/10.1007/s13366-011-0008-z
-
R. Lopez and M. I. Munteanu, Minimal translation surfaces in
$Sol_3$ , J. Math. Soc. Japan 64 (2012), no. 3, 985-1003. https://doi.org/10.2969/jmsj/06430985 - R. Lopez and M. Moruz, Translation and homothetical surfaces in Euclidean space with constant curvature, J. Korean Math. Soc. 52 (2015), no. 3, 523-535. https://doi.org/10.4134/JKMS.2015.52.3.523
- H. Meng and H. Liu, Factorable surfaces in Minkowski space, Bull. Korean Math. Soc. 46 (2009), no. 1, 155-169. https://doi.org/10.4134/BKMS.2009.46.1.155
- Z. Milin-Sipus, Translation surfaces of constant curvatures in a simply isotropic space, Period. Math. Hungar. 68 (2014), no. 2, 160-175. https://doi.org/10.1007/s10998-014-0027-2
- M. I. Munteanu, O. Palmas, and G. Ruiz-Hernandez, Minimal translation hypersurfaces in Euclidean spaces, Mediterr. J. Math. 13 (2016), no. 5, 2659-2676. https://doi.org/10.1007/s00009-015-0645-9
- H. Pottmann and K. Opitz, Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces, Comput. Aided Geom. Design 11 (1994), no. 6, 655-674. https://doi.org/10.1016/0167-8396(94)90057-4
- H. Pottmann, P. Grohs, and N. J. Mitra, Laguerre minimal surfaces, isotropic geometry and linear elasticity, Adv. Comput. Math. 31 (2009), no. 4, 391-419. https://doi.org/10.1007/s10444-008-9076-5
- H. Sachs, Isotrope Geometrie des Raumes, Vieweg Verlag, Braunschweig, 1990.
- I. Van de Woestyne, Minimal homothetical hypersurfaces of a semi-Euclidean space, Results. Math. 27 (1995), 333-342. https://doi.org/10.1007/BF03322837
-
D. W. Yoon, Minimal translation surfaces in
${\mathbb{H}^2}{\time}{\mathbb{R}}$ , Taiwanese J. Math. 17 (2013), no. 5, 1545-1556. https://doi.org/10.11650/tjm.17.2013.2425 - D. W. Yoon and J. W. Lee, Translation invariant surfaces in the 3-dimensional Heisenberg group, Bull. Iranian Math. Soc. 40 (2014), no. 6, 1373-1385.
- Y. Yu and H. Liu, The factorable minimal surfaces, Proceedings of the Eleventh International Workshop on Differential Geometry, 33-39, Kyungpook Nat. Univ., Taegu, 2007.
- P. Zong, L. Xiao, and H. L. Liu, Affne factorable surfaces in three-dimensional Euclidean space, Acta Math. Sinica (Chin. Ser.) 58 (2015), no. 2, 329-336.