References
- M. E. Aydin, A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom. 107 (2016), no. 3, 603-615. https://doi.org/10.1007/s00022-015-0292-0
-
Ch. Baba-Hamed, M. Bekkar, and H. Zoubir, Translation surfaces in the three dimensional Lorentz-Minkowski space satisfying
${\Delta}r_i$ =$Ar_i$ , Int. J. Math. Anal. 4 (2010), no. 17, 797-808. -
M. Bekkar and B. Senoussi, Translation surfaces in the 3-dimensional space satisfying
${\Delta}^{III}r_i$ =${\mu}_ir_i4 , J. Geom. 103 (2012), no. 3, 367-374. https://doi.org/10.1007/s00022-012-0136-0 -
B. Bukcu, D. W. Yoon, and M. K. Karacan, Translation surfaces in the 3-dimensional simply isotropic space
$II{\frac{1}{3}}$ satisfying${\Delta}^{III}x_i$ =${\lambda}_ix_i$ , Konuralp J. Math. 4 (2016), no. 1, 275-281. - B. Y. Chen, A report on submanifold of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337.
- F. Dillen, J. Pas, and L. Vertraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J. 13 (1990), no. 1, 10-21. https://doi.org/10.2996/kmj/1138039155
- F. Dillen, J. Pas, and L. Vertraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica 18 (1990), no. 3, 239-246.
- O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata 34 (1990), no. 2, 105-112. https://doi.org/10.1007/BF00147319
-
G. Kaimakamis, B. Papantoniou, and K. Petoumenos, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying
${\Delta}^{III}r$ = Ar, Bull. Greek Math. Soc. 50 (2005), 75-90. -
M. K. Karacan, D. W. Yoon, and B. Bukcu, Translation surfaces in the three dimensional simply isotropic space
$II{\frac{1}{3}}$ , Int. J. Geom. Methods Mod. Phys. 13 (2016), no. 7, 1650088, 9 pp. - H. Sachs, Isotrope geometrie des raumes, Vieweg Verlag, Braunschweig, 1990.
-
B. Senoussi and M. Bekkar, Helicoidal surfaces with
${\Delta}^Jr$ = Ar in 3-dimensional Euclidean space, Stud. Univ. Babes-Bolyai Math. 60 (2015), no. 13, 437-448. - Z. M. 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
- K. Strubecker, Differentialgeometrie des Isotropen raumes III. Flachentheorie, Math. Z. 48 (1942), 369-427. https://doi.org/10.1007/BF01180022
- T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. https://doi.org/10.2969/jmsj/01840380
- D.W. Yoon, On the Gauss map of translation surfaces in Minkowski 3-space, Taiwanese J. Math. 6 (2002), no. 3, 389-398. https://doi.org/10.11650/twjm/1500558304
- D.W. Yoon, Some classification of translation surfaces in Galilean 3-Space, Int. J. Math. Anal. 6 (2012), no. 28, 1355-1361.