References
- R.A. Abdel-Baky and Y. Unluturk, A study on classification of translation surfaces in pseudo-Galilean 3-space, J. Coupl. Syst. Multi. Dynm. 6 (2018), no. 3, 233-240.
- M. E. Aydin, M. A. Kulahci, and A. O. Ogrenmis, Constant curvature translation surfaces in Galilean 3-space, Int. Electron. J. Geom. 12(2019), no.1, 9-19. https://doi.org/10.36890/iejg.545741
- C. Baikoussis and T. Koufogioros, Helicoidal surface with prescribed mean or Gauss curvature, J. Geom. 63 (1998), 25-29. https://doi.org/10.1007/BF01221235
- A. Cakmak, M.K. Karacan, S. Kiziltug, and D.W. Yoon, Corrigendum to "Translation surfaces in the 3-dimensional Galilean space satisfying ΔII xi = λixi", Bull. Korean Math. Soc. 56 (2019), no. 2, 549-554. https://doi.org/10.4134/BKMS.B180817
- I. Castro, I. Castro-Infantes, and J. Castro-Infantes, Curves in the Lorentz-Minkowski plane with curvature depending on their position, Open Mathematics 18 (2020), 749-770. https://doi.org/10.1515/math-2020-0043.
- J. G. Darboux, Theorie generale des surfaces, Livre I, Gauthier-Villars, Paris, 1914.
- F. Dillen, L. Verstraelen, and G. Zafindratafa, A generalization of the translation surfaces of Scherk, Different. Geom. in Honor of Radu Rosca: Meeting on Pure and Appl. Different. Geom. (Leuven, Belgium, 1989), KU Leuven, Department Wiskunde (1991), pp. 107 - 109.
- F. Dillen, I. Van de Woestyne, L. Verstraelen, and J. T. Walrave, The surface of Scherk in E3: A special case in the class of minimal surfaces defined as the sum of two curves, Bull. Inst. Math. Acad. Sin. 4 (1998), 257-267.
- W. Goemans and I. Van de Woestyne, Translation and homothetical lightlike hypersurfaces of semi-Euclidean space, Kuwait J. Sci. Eng. 38 (2011), no. 2A, 35-42.
- T. Hasanis, Translation surfaces with non-zero constant mean curvature in Euclidean space, J. Geom. 110 (2019), Number 20. https://doi.org/10.1007/s00022-019-0476-0.
- T. Hasanis and R. Lopez, Classification and construction of minimal translation surfaces in Euclidean space, Results Math 75 (2020), Number 2. https://doi.org/10.1007/s00025-019-1128-2
- T. Hasanis and R. Lopez, Translation surfaces in Euclidean space with constant Gaussian curvature, Commun. Anal. Geom., in press.
- S. Kaya and R. Lopez, Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space, preprint(2020). arXiv:2005.07663v1.
- A. Kelleci, Translation-factorable surfaces with vanishing curvatures in Galilean 3-spaces, Int. J. Maps. Math. 4 (2021), no. 1, 14-26.
- K. Kenmotsu, Surface of revolution with prescribed mean curvature, Tohoku Math. J. 32 (1980), 147-153. https://doi.org/10.2748/tmj/1178229688
- O. Kobayashi, Maximal surfaces in the 3-dimensional Minkowski space L3, Tokyo J. Math. 6 (1983), 297-309.
- B.P. Lima, N.L. Santos, and P.A. Sousa, Generalized translation hypersurfaces in Euclidean space, J. Math. Anal. Appl. 470 (2019), 1129-1135. https://doi.org/10.1016/j.jmaa.2018.10.053
- H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141-149. https://doi.org/10.1007/BF01229219
- H. Liu and S. D. Jung, Affine translation surfaces with constant mean curvature in Euclidean 3-space, J. Geom. 108 (2017), 423-428. https://doi.org/10.1007/s00022-016-0348-9.
- H. Liu and Y. Yu, Affine translation surfaces in Euclidean 3-space, Proc. Japan Acad. Ser. A, Math. Sci. 89 (2013), 111-113.
- R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom. 7 (2014), no. 1, 44-107. https://doi.org/10.36890/iejg.594497
- 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
- R. Lopez and O. Perdomo, Minimal translation surfaces in Euclidean space, J. Geom. Anal., 27 (2017), no 4, 2926-2937. https://doi.org/10.1007/s12220-017-9788-1
- Z. Milin-Sipus, On a certain class of translation surfaces in a pseudo-Galilean space, Int. Mat. Forum 6 (2012), no. 23, 1113-1125.
- Z. Milin-Sipus and B. Divjak, Translation surface in the Galilean space, Glas. Mat. Ser. III 46 (2011), no. 2, 455-469. https://doi.org/10.3336/gm.46.2.14
- Z. Milin-Sipus and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Sci. (2012), Art ID375264, 28pp.
- E. Molnar, The projective interpretation of the eight G3-dimensional homogeneous geometries, Beitr. Algebra Geom. 38 (1997), no. 2, 261-288.
- M. Moruz and M. I. Munteanu, Minimal translation hypersurfaces in E4, J. Math. Anal. and Appl. 439 (2016), no 2, 798-812. https://doi.org/10.1016/j.jmaa.2016.02.077
- M. I. Munteanu, O. Palmas, and G. Ruiz-Hernandez, Minimal translation hypersurfaces in Euclidean spaces, Mediterr. J. Math. 13 (2016), 2659-2676. https://doi.org/10.1007/s00009-015-0645-9
- B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
- A. Onishchick and R. Sulanke, Projective and Cayley-Klein Geometries, Springer, 2006.
- O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, 1984.
- G. Ruiz-Hernandez, Translation hypersurfaces whose curvature depends partially on its variables, J. Math. Anal. Appl. 497 (2021), 124913. https://doi.org/10.1016/j.jmaa.2020.124913
- T. Sahin, Relaxed elastic line on an oriented surface in the Galilean space, Int. J. Adv. Appl. Math. and Mech. 6 (2019), no. 3, 35-41.
- H. F. Scherk, Bemerkungen uber die kleinste Flache innerhalb gegebener Grenzen, J. reine und angew. Math. 13 (1835), 185-208.
- K. Seo, Translation hypersurfaces with constant curvature in space forms, Osaka J. Math. 50 (2013), 631-641.
- I. Van de Woestijne, Minimal surfaces of the 3-dimensional Minkowski space. Geometry and topology of submanifolds, II (Avignon, 1988), World Sci. Publ., Teaneck, NJ, 1990, p. 344-369.
- L. Verstraelen, J. Walrave, and S. Yaprak, The minimal translation surfaces in Euclidean space, Soochow J. Math. 20 (1994), 77-82.
- I. M. Yaglom, A simple non-Euclidean geometry and its physical basis, Springer-Verlag, New York, 1979.
- D. Yang, J. Zhang, and Y. Fu, A note on minimal translation graphs in Euclidean space, Mathematics 7 (2019), 889. https://doi.org/10.3390/math7100889
- D.W. Yoon, Some classification of translation surfaces in Galilean 3-space, Int. J. Math. Analy. 6 (2012), no. 28, 1355-1361.
- D.W. Yoon, Weighted minimal translation surfaces in the Galilean space with density, Open Math. 15 (2017), 459-466. https://doi.org/10.1515/math-2017-0043