Yıl: 2022 Cilt: Sayı: 40 Sayfa Aralığı: 1 - 11 Metin Dili: İngilizce DOI: 10.53570/jnt.1137525 İndeks Tarihi: 30-10-2022

Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures

Öz:
We study the so-called factorable surfaces in the pseudo-Galilean space, the graphs of the product of two functions of one variable. We then classify these surfaces when the mean and Gaussian curvatures are functions of one variable.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] O. Giering, Vorlesungen ̈uber h ̈ohere Geometrie, Friedr Vieweg & Sohn, Braunschweig, Germany, 1982.
  • [2] B. Divjak and Z. Milin-Sipus, Special Curves on Ruled Surfaces in Galilean and Pseudo-Galilean Spaces, Acta Mathematica Hungarica 98 (1) (2003) 203–215.
  • [3] E. M ́olnar, The Projective Interpretation of the Eight 3-Dimensional Homogeneous Geometries, Beitrage zur Algebra und Geometrie 38 (2) (1997) 261–288.
  • [4] A. Onishchick and R. Sulanke, Projective and Cayley-Klein Geometries, Springer, 2006.
  • [5] I. M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979.
  • [6] B. Y. Chen, G. E. Vˆılcu, Geometric Classifications of Homogeneous Production Functions, Ap- plied Mathematics and Computation 225 (2013) 345–351.
  • [7] B. Y. Chen, A Note on Homogeneous Production Models, Kragujevac Journal of Mathematics 36 (1) (2012) 41–43.
  • [8] B. Y. Chen, Solutions to Homogeneous Monge-Amp`ere Equations of Homothetic Functions and Their Applications to Production Models in Economics, Journal of Mathematical Analysis and Applications 411 (2014) 223–229.
  • [9] M. J. P. Cullen, R. J. Douglas, Applications of the Monge-Amp`e re equation and Monge transport problem to meterology and oceanography, In: L. A. Caffarelli, M. Milman (eds.), NSF-CBMS Conference on the Monge Amp‘ere Equation, Applications to Geometry and Optimization, July 9-13, Florida Atlantic University, 1997, pp. 33–54.
  • [10] D. Gilbarg, N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Berlin, Springer-Verlag, 1983.
  • [11] V. Ushakov, The Explicit General Solution of Trivial Monge-Amp`ere Equation, Commentarii Mathematici Helvetici 75 (2000) 125–133.
  • [12] M. E. Aydın, M. Alyamac K ̈ulahcı, A.O. ̈O ̆grenmis, Constant Curvature Translation Surfaces in Galilean 3-Space, International Electronic Journal of Geometry 12 (1) (2019) 9–19.
  • [13] A. Kelleci, Translation-Factorable Surfaces with Vanishing Curvatures in Galilean 3-Spaces, In- ternational Journal of Maps in Mathematics 4 (1) (2021) 14–26.
  • [14] Z. Milin-Sipus, B. Divjak, Translation Surface in the Galilean Space, Glasnik Matematicki 46 (66) (2011) 455–469.
  • [15] Z. Milin-Sipus, On a Certain Class of Translation Surfaces in a Pseudo-Galilean Space, Interna- tional Mathematical Forum 6 (23) (2011) 1113–1125.
  • [16] D. W. Yoon, Some Classification of Translation Surfaces in Galilean 3-Space, International Jour- nal of Mathematical Analysis 6 (28) (2012) 1355–1361.
  • [17] M.E. Aydın, S. Aykurt Sepet, H. G ̈un Bozok, Translation Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures, Honam Mathematical Journal 44 (1) (2022) 36–51.
  • [18] G. Ruiz-Hern ́andez, Translation Hypersurfaces whose Curvature Depends Partially on Its Vari- ables, Journal of Mathematical Analysis and Applications 497 (2) (2021) 124913.
  • [19] C. Baikoussis, T. Koufogioros, Helicoidal Surface with Prescribed Mean or Gauss Curvature, Journal of Geometry 63 (1998) 25–29.
  • [20] K. Kenmotsu, Surface of Revolution with Prescribed Mean Curvature, Tohoku Mathematical Journal 32 (1980) 147–153.
  • [21] I. Van de Woestyne, Minimal Homothetical Hypersurfaces of a Semi-Euclidean Space, Results in Mathematics 27 (1995) 333–342.
  • [22] H. S. Abdel-Aziz, M. Khalifa Saad, A. Ali Haytham, Affine Factorable Surfaces in Pseudo- Galilean Space, arXiv:1812.00765v1[math.GM].
  • [23] P. Bansal, M. H. Shahid, On Classification of Factorable Surfaces in Galilean Space G3, Jordan Journal of Mathematics and Statistics 12 (3) (2019) 289–306.
  • [24] M. S. Lone, Homothetical Surfaces in Three Dimensional Pseudo-Galilean Spaces Satisfying △II xi = λixi, Advances in Applied Clifford Algebras 29 (92) (2019).
  • [25] M. E. Aydın, A. O. ̈O ̆grenmis, M. Erg ̈ut, Classification of Factorable Surfaces in the Pseudo- Galilean Space, Glasnik Matematicki 70 (50) (2015) 441–451.
  • [26] M. E. Aydın, M. Alyamac K ̈ulahcı, A. O. ̈O ̆grenmis, Non-Zero Constant Curvature Factorable Surfaces in Pseudo-Galilean Space, Communications of the Korean Mathematical Society 33 (1) (2018) 247–259.
  • [27] B. Divjak, Z. Milin-Sipus, Minding Isometries of Ruled Surfaces in Pseudo-Galilean Space, Jour- nal of Geometry 77 (2003) 35–47.
APA aykurt sepet s, GÜN BOZOK H, Aydin M (2022). Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. , 1 - 11. 10.53570/jnt.1137525
Chicago aykurt sepet sezin,GÜN BOZOK Hülya,Aydin Muhittin Evren Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. (2022): 1 - 11. 10.53570/jnt.1137525
MLA aykurt sepet sezin,GÜN BOZOK Hülya,Aydin Muhittin Evren Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. , 2022, ss.1 - 11. 10.53570/jnt.1137525
AMA aykurt sepet s,GÜN BOZOK H,Aydin M Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. . 2022; 1 - 11. 10.53570/jnt.1137525
Vancouver aykurt sepet s,GÜN BOZOK H,Aydin M Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. . 2022; 1 - 11. 10.53570/jnt.1137525
IEEE aykurt sepet s,GÜN BOZOK H,Aydin M "Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures." , ss.1 - 11, 2022. 10.53570/jnt.1137525
ISNAD aykurt sepet, sezin vd. "Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures". (2022), 1-11. https://doi.org/10.53570/jnt.1137525
APA aykurt sepet s, GÜN BOZOK H, Aydin M (2022). Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory, (40), 1 - 11. 10.53570/jnt.1137525
Chicago aykurt sepet sezin,GÜN BOZOK Hülya,Aydin Muhittin Evren Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory , no.40 (2022): 1 - 11. 10.53570/jnt.1137525
MLA aykurt sepet sezin,GÜN BOZOK Hülya,Aydin Muhittin Evren Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory, vol., no.40, 2022, ss.1 - 11. 10.53570/jnt.1137525
AMA aykurt sepet s,GÜN BOZOK H,Aydin M Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory. 2022; (40): 1 - 11. 10.53570/jnt.1137525
Vancouver aykurt sepet s,GÜN BOZOK H,Aydin M Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory. 2022; (40): 1 - 11. 10.53570/jnt.1137525
IEEE aykurt sepet s,GÜN BOZOK H,Aydin M "Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures." Journal of New Theory, , ss.1 - 11, 2022. 10.53570/jnt.1137525
ISNAD aykurt sepet, sezin vd. "Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures". Journal of New Theory 40 (2022), 1-11. https://doi.org/10.53570/jnt.1137525