Curvatures of the Factorable Hypersurface
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Published
Dec 8, 2020
Page:
76-82
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Erhan Güler
Department of Mathematics, Faculty of Sciences, Bartın University, 74100 Bartın, Turkey.
Abstract
The curvatures of a factorable hypersurface are introduced in the four-dimensional Euclidean space. It is also given some relations on of the factorable hypersurface.
Keywords:
Four-space, factorable hypersurface, fourth fundamental form.
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Original Research Article
References
Arslan K, Bayram B, Bulca B, Öztürk G. On translation surfaces in 4-dimensional Euclidean space. Acta Comm. Univ. Tartuensis Math. 2016;20(2):123–133.
Aydın ME. Constant curvature factorable surfaces in 3-dimensional isotropic space. J. Korean Math. Soc. 2018;55(1):59–71.
Aydın ME, Öğrenmiş AO. Linear Weingarten factorable surfaces in isotropic spaces. Stud. Univ. Babeş-Bolyai Math. 2017;62(2):261–268.
Aydın ME, Külahcı M, Öğrenmiş AO. Non-zero constant curvature factorable surfaces in pseudo-Galilean space, Comm. Korean Math. Soc. 2018;33(1):247–259.
Aydın ME, Öğrenmiş AO, Ergüt M. Classification of factorable surfaces in the Pseudo-Galilean 3-space. Glasnik Matematicki. 2015;50(70):441–451.
Baba-Hamed C, Bekkar M, Zoubir H. Translation surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying Δri=λiri. Int. J. Math. Analysis. 2010;4(17):797–808.
Bekkar M., Senoussi B. Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying Δri=λiri. J. Geom. 2012;103(1):17–29.
Bulca B, Arslan K, Bayram BK, Öztürk G. Spherical product surface in E^4. Ann. St. Univ. Ovidius Constanta. 2012;20(1):41–54.
Büyükkütük S, Öztürk G. Spacelike factorable surfaces in four-dimensional Minkowski space. Bull. Math. Anal. Appl. 2017;9(4):12–20.
Dillen F, Verstraelen L, 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, Department Wiskunde. 1991;107–109.
Dillen F, Van de Woestyne I, Verstraelen L, Walrave JT. 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. 1998;26:257–267.
Inoguchi J, López R, Munteanu M. Minimal translation surfaces in the Heisenberg group Nil3. Geom Dedicata. 2012;161(1):221–231.
Jiu L, Sun H. On minimal homothetical hypersurfaces. Colloq. Math. 2007;109(2):239–249.
Liu H. Translation surfaces with dependent Gaussian and mean curvature in 3-dimensional spaces. J. Northeast Univ. Tech. 1993;14(1):88–93.
Liu H. Translation surfaces with constant mean curvature in 3-dimensional spaces. J. Geom. 1999;64:141–149.
Lopez R. Moruz M. Translation and homothetical surfaces in Euclidean space with constant curvature. J. Korean Math. Soc. 2015;52(3):523–535.
Meng H, Liu H. Factorable surfaces in 3-Minkowski space. Bull. Korean Math. Soc. 2009;46(1):155–169.
Moruz M, Munteanu M. Minimal translation hypersurfaces in E^4.J. Math. Anal. Appl. 2016;439:798–812.
Munteanu M, Nistor AI. On the geometry of the second fundamental form of translation surfaces in E^3. Houston J. Math. 2011;37:1087–1102.
Munteanu M, Palmas O, Ruiz-Hernandez G. Minimal translation hypersurfaces in Euclidean space. Mediterr. J. Math. 2016;13:2659–2676.
Scherk HF. Bemerkungen ber die Kleinste fläche innerhalb Gegebener Grenzen, J. R. Angew.Math. 1935;13:185–208.
Turhan E, Altay G. Maximal and minimal surfaces of factorable surfaces in Heis3. Int. J. Open Probl. Comput. Sci. Math. 2010;3(2) :200–212.
Van de Woestyne I. Minimal homothetical hypersurfaces of a semi-Euclidean space. Results Math. 1995;27(3-4):333–342.
Yu Y, Liu H. The factorable minimal surfaces. Proceedings of the Eleventh International Workshop on Differential Geometry. Kyungpook Nat. Univ., Taegu. 2007;33–39.
Zong P, Xiao L, Liu HL. Affine factorable surfaces in three-dimensional Euclidean space. (Chinese) Acta Math. Sinica (Chin. Ser.). 2015;58(2):329–336.
Aydın ME. Constant curvature factorable surfaces in 3-dimensional isotropic space. J. Korean Math. Soc. 2018;55(1):59–71.
Aydın ME, Öğrenmiş AO. Linear Weingarten factorable surfaces in isotropic spaces. Stud. Univ. Babeş-Bolyai Math. 2017;62(2):261–268.
Aydın ME, Külahcı M, Öğrenmiş AO. Non-zero constant curvature factorable surfaces in pseudo-Galilean space, Comm. Korean Math. Soc. 2018;33(1):247–259.
Aydın ME, Öğrenmiş AO, Ergüt M. Classification of factorable surfaces in the Pseudo-Galilean 3-space. Glasnik Matematicki. 2015;50(70):441–451.
Baba-Hamed C, Bekkar M, Zoubir H. Translation surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying Δri=λiri. Int. J. Math. Analysis. 2010;4(17):797–808.
Bekkar M., Senoussi B. Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying Δri=λiri. J. Geom. 2012;103(1):17–29.
Bulca B, Arslan K, Bayram BK, Öztürk G. Spherical product surface in E^4. Ann. St. Univ. Ovidius Constanta. 2012;20(1):41–54.
Büyükkütük S, Öztürk G. Spacelike factorable surfaces in four-dimensional Minkowski space. Bull. Math. Anal. Appl. 2017;9(4):12–20.
Dillen F, Verstraelen L, 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, Department Wiskunde. 1991;107–109.
Dillen F, Van de Woestyne I, Verstraelen L, Walrave JT. 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. 1998;26:257–267.
Inoguchi J, López R, Munteanu M. Minimal translation surfaces in the Heisenberg group Nil3. Geom Dedicata. 2012;161(1):221–231.
Jiu L, Sun H. On minimal homothetical hypersurfaces. Colloq. Math. 2007;109(2):239–249.
Liu H. Translation surfaces with dependent Gaussian and mean curvature in 3-dimensional spaces. J. Northeast Univ. Tech. 1993;14(1):88–93.
Liu H. Translation surfaces with constant mean curvature in 3-dimensional spaces. J. Geom. 1999;64:141–149.
Lopez R. Moruz M. Translation and homothetical surfaces in Euclidean space with constant curvature. J. Korean Math. Soc. 2015;52(3):523–535.
Meng H, Liu H. Factorable surfaces in 3-Minkowski space. Bull. Korean Math. Soc. 2009;46(1):155–169.
Moruz M, Munteanu M. Minimal translation hypersurfaces in E^4.J. Math. Anal. Appl. 2016;439:798–812.
Munteanu M, Nistor AI. On the geometry of the second fundamental form of translation surfaces in E^3. Houston J. Math. 2011;37:1087–1102.
Munteanu M, Palmas O, Ruiz-Hernandez G. Minimal translation hypersurfaces in Euclidean space. Mediterr. J. Math. 2016;13:2659–2676.
Scherk HF. Bemerkungen ber die Kleinste fläche innerhalb Gegebener Grenzen, J. R. Angew.Math. 1935;13:185–208.
Turhan E, Altay G. Maximal and minimal surfaces of factorable surfaces in Heis3. Int. J. Open Probl. Comput. Sci. Math. 2010;3(2) :200–212.
Van de Woestyne I. Minimal homothetical hypersurfaces of a semi-Euclidean space. Results Math. 1995;27(3-4):333–342.
Yu Y, Liu H. The factorable minimal surfaces. Proceedings of the Eleventh International Workshop on Differential Geometry. Kyungpook Nat. Univ., Taegu. 2007;33–39.
Zong P, Xiao L, Liu HL. Affine factorable surfaces in three-dimensional Euclidean space. (Chinese) Acta Math. Sinica (Chin. Ser.). 2015;58(2):329–336.