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

Year 2022, Issue: 40, 1 - 11, 30.09.2022

Sezin Aykurt Sepet , Hülya Gün Bozok , Muhittin Evren Aydın

https://doi.org/10.53570/jnt.1137525
Cited By: 1

Abstract

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.

Keywords

Pseudo-Galilean space factorable surface Gaussian curvature mean curvature

References

  • O. Giering, Vorlesungen über höhere Geometrie, Friedr Vieweg & Sohn, Braunschweig, Germany, 1982.
  • 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.
  • E. M_olnar, The Projective Interpretation of the Eight 3-Dimensional Homogeneous Geometries, Beitrage zur Algebra und Geometrie 38 (2) (1997) 261-288.
  • A. Onishchick and R. Sulanke, Projective and Cayley-Klein Geometries, Springer, 2006.
  • I. M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979.
  • B. Y. Chen, G. E. Vîlcu, Geometric Classifications of Homogeneous Production Functions, Applied Mathematics and Computation 225 (2013) 345-351.
  • B. Y. Chen, A Note on Homogeneous Production Models, Kragujevac Journal of Mathematics 36 (1) (2012) 41-43.
  • B. Y. Chen, Solutions to Homogeneous Monge-Ampère Equations of Homothetic Functions and Their Applications to Production Models in Economics, Journal of Mathematical Analysis and Applications 411 (2014) 223-229.
  • M. J. P. Cullen, R.J. Douglas, Applications of the Monge-Ampère equation and Monge transport problem to meterology and oceanography, In: L. A. Ca_arelli, 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.
  • D. Gilbarg, N. S. Trudinger, Elliptic Partial Di_erential Equations of Second Order, Berlin, Springer-Verlag, 1983.
  • V. Ushakov, The Explicit General Solution of Trivial Monge-Amp_ere Equation, Commentarii Mathematici Helvetici 75 (2000) 125-133.
  • M. E. Aydın, M. Alyamac Külahcı, A.O. Öğrenmis, Constant Curvature Translation Surfaces in Galilean 3-Space, International Electronic Journal of Geometry 12 (1) (2019) 9-19.
  • A. Kelleci, Translation-Factorable Surfaces with Vanishing Curvatures in Galilean 3-Spaces, International Journal of Maps in Mathematics 4 (1) (2021) 14-26.
  • Z. Milin-Sipus, B. Divjak, Translation Surface in the Galilean Space, Glasnik Matematicki 46 (66) (2011) 455-469.
  • Z. Milin-Sipus, On a Certain Class of Translation Surfaces in a Pseudo-Galilean Space, International Mathematical Forum 6 (23) (2011) 1113-1125.
  • D. W. Yoon, Some Classification of Translation Surfaces in Galilean 3-Space, International Journal of Mathematical Analysis 6 (28) (2012) 1355-1361.
  • M.E. Aydın, S. Aykurt Sepet, H. Gün Bozok, Translation Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures, Honam Mathematical Journal 44 (1) (2022) 36-51.
  • G. Ruiz-Hernández, Translation Hypersurfaces whose Curvature Depends Partially on Its Variables, Journal of Mathematical Analysis and Applications 497 (2) (2021) 124913.
  • C. Baikoussis,T. Koufogioros, Helicoidal Surface with Prescribed Mean or Gauss Curvature, Journal of Geometry 63 (1998) 25-29.
  • K. Kenmotsu, Surface of Revolution with Prescribed Mean Curvature, Tohoku Mathematical Journal 32 (1980) 147-153.
  • I. Van de Woestyne, Minimal Homothetical Hypersurfaces of a Semi-Euclidean Space, Results in Mathematics 27 (1995) 333-342.
  • H. S. Abdel-Aziz, M. Khalifa Saad, A. Ali Haytham, Affine Factorable Surfaces in Pseudo-Galilean Space, arXiv:1812.00765v1[math.GM].
  • P. Bansal, M. H. Shahid, On Classi_cation of Factorable Surfaces in Galilean Space G3, Jordan Journal of Mathematics and Statistics 12 (3) (2019) 289-306.
  • M. S. Lone, Homothetical Surfaces in Three Dimensional Pseudo-Galilean Spaces Satisfying $\vartriangle ^{II}\mathbf{x}_{i}=\lambda_{i}\mathbf{x}_{i}$, Advances in Applied Clifiord Algebras 29 (92) (2019).
  • M. E. Aydın, A. O. Öğrenmis, M. Ergüt, Classification of Factorable Surfaces in the Pseudo-Galilean Space, Glasnik Matematicki 70 (50) (2015) 441-451.
  • M. E. Aydın, M. Alyamac Külahcı, A. O. Öğrenmis, Non-Zero Constant Curvature Factorable Surfaces in Pseudo-Galilean Space, Communications of the Korean Mathematical Society 33 (1) (2018) 247-259.
  • B. Divjak, Z. Milin-Sipus, Minding Isometries of Ruled Surfaces in Pseudo-Galilean Space, Journal of Geometry 77 (2003) 35-47.

Year 2022, Issue: 40, 1 - 11, 30.09.2022

Sezin Aykurt Sepet , Hülya Gün Bozok , Muhittin Evren Aydın

https://doi.org/10.53570/jnt.1137525
Cited By: 1

Abstract

References

  • O. Giering, Vorlesungen über höhere Geometrie, Friedr Vieweg & Sohn, Braunschweig, Germany, 1982.
  • 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.
  • E. M_olnar, The Projective Interpretation of the Eight 3-Dimensional Homogeneous Geometries, Beitrage zur Algebra und Geometrie 38 (2) (1997) 261-288.
  • A. Onishchick and R. Sulanke, Projective and Cayley-Klein Geometries, Springer, 2006.
  • I. M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979.
  • B. Y. Chen, G. E. Vîlcu, Geometric Classifications of Homogeneous Production Functions, Applied Mathematics and Computation 225 (2013) 345-351.
  • B. Y. Chen, A Note on Homogeneous Production Models, Kragujevac Journal of Mathematics 36 (1) (2012) 41-43.
  • B. Y. Chen, Solutions to Homogeneous Monge-Ampère Equations of Homothetic Functions and Their Applications to Production Models in Economics, Journal of Mathematical Analysis and Applications 411 (2014) 223-229.
  • M. J. P. Cullen, R.J. Douglas, Applications of the Monge-Ampère equation and Monge transport problem to meterology and oceanography, In: L. A. Ca_arelli, 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.
  • D. Gilbarg, N. S. Trudinger, Elliptic Partial Di_erential Equations of Second Order, Berlin, Springer-Verlag, 1983.
  • V. Ushakov, The Explicit General Solution of Trivial Monge-Amp_ere Equation, Commentarii Mathematici Helvetici 75 (2000) 125-133.
  • M. E. Aydın, M. Alyamac Külahcı, A.O. Öğrenmis, Constant Curvature Translation Surfaces in Galilean 3-Space, International Electronic Journal of Geometry 12 (1) (2019) 9-19.
  • A. Kelleci, Translation-Factorable Surfaces with Vanishing Curvatures in Galilean 3-Spaces, International Journal of Maps in Mathematics 4 (1) (2021) 14-26.
  • Z. Milin-Sipus, B. Divjak, Translation Surface in the Galilean Space, Glasnik Matematicki 46 (66) (2011) 455-469.
  • Z. Milin-Sipus, On a Certain Class of Translation Surfaces in a Pseudo-Galilean Space, International Mathematical Forum 6 (23) (2011) 1113-1125.
  • D. W. Yoon, Some Classification of Translation Surfaces in Galilean 3-Space, International Journal of Mathematical Analysis 6 (28) (2012) 1355-1361.
  • M.E. Aydın, S. Aykurt Sepet, H. Gün Bozok, Translation Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures, Honam Mathematical Journal 44 (1) (2022) 36-51.
  • G. Ruiz-Hernández, Translation Hypersurfaces whose Curvature Depends Partially on Its Variables, Journal of Mathematical Analysis and Applications 497 (2) (2021) 124913.
  • C. Baikoussis,T. Koufogioros, Helicoidal Surface with Prescribed Mean or Gauss Curvature, Journal of Geometry 63 (1998) 25-29.
  • K. Kenmotsu, Surface of Revolution with Prescribed Mean Curvature, Tohoku Mathematical Journal 32 (1980) 147-153.
  • I. Van de Woestyne, Minimal Homothetical Hypersurfaces of a Semi-Euclidean Space, Results in Mathematics 27 (1995) 333-342.
  • H. S. Abdel-Aziz, M. Khalifa Saad, A. Ali Haytham, Affine Factorable Surfaces in Pseudo-Galilean Space, arXiv:1812.00765v1[math.GM].
  • P. Bansal, M. H. Shahid, On Classi_cation of Factorable Surfaces in Galilean Space G3, Jordan Journal of Mathematics and Statistics 12 (3) (2019) 289-306.
  • M. S. Lone, Homothetical Surfaces in Three Dimensional Pseudo-Galilean Spaces Satisfying $\vartriangle ^{II}\mathbf{x}_{i}=\lambda_{i}\mathbf{x}_{i}$, Advances in Applied Clifiord Algebras 29 (92) (2019).
  • M. E. Aydın, A. O. Öğrenmis, M. Ergüt, Classification of Factorable Surfaces in the Pseudo-Galilean Space, Glasnik Matematicki 70 (50) (2015) 441-451.
  • M. E. Aydın, M. Alyamac Külahcı, A. O. Öğrenmis, Non-Zero Constant Curvature Factorable Surfaces in Pseudo-Galilean Space, Communications of the Korean Mathematical Society 33 (1) (2018) 247-259.
  • B. Divjak, Z. Milin-Sipus, Minding Isometries of Ruled Surfaces in Pseudo-Galilean Space, Journal of Geometry 77 (2003) 35-47.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Sezin Aykurt Sepet 0000-0003-1521-6798

Hülya Gün Bozok 0000-0002-7370-5760

Muhittin Evren Aydın 0000-0001-9337-8165

Publication Date September 30, 2022
Submission Date June 29, 2022
Published in Issue Year 2022 Issue: 40

Cite

APA Aykurt Sepet, S., Gün Bozok, H., & Aydın, M. E. (2022). Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory(40), 1-11. https://doi.org/10.53570/jnt.1137525
AMA Aykurt Sepet S, Gün Bozok H, Aydın ME. Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. JNT. September 2022;(40):1-11. doi:10.53570/jnt.1137525
Chicago Aykurt Sepet, Sezin, Hülya Gün Bozok, and Muhittin Evren Aydın. “Factorable Surfaces in Pseudo-Galilean Space With Prescribed Mean and Gaussian Curvatures”. Journal of New Theory, no. 40 (September 2022): 1-11. https://doi.org/10.53570/jnt.1137525.
EndNote Aykurt Sepet S, Gün Bozok H, Aydın ME (September 1, 2022) Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. Journal of New Theory 40 1–11.
IEEE S. Aykurt Sepet, H. Gün Bozok, and M. E. Aydın, “Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures”, JNT, no. 40, pp. 1–11, September 2022, doi: 10.53570/jnt.1137525.
ISNAD Aykurt Sepet, Sezin et al. “Factorable Surfaces in Pseudo-Galilean Space With Prescribed Mean and Gaussian Curvatures”. Journal of New Theory 40 (September 2022), 1-11. https://doi.org/10.53570/jnt.1137525.
JAMA Aykurt Sepet S, Gün Bozok H, Aydın ME. Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. JNT. 2022;:1–11.
MLA Aykurt Sepet, Sezin et al. “Factorable Surfaces in Pseudo-Galilean Space With Prescribed Mean and Gaussian Curvatures”. Journal of New Theory, no. 40, 2022, pp. 1-11, doi:10.53570/jnt.1137525.
Vancouver Aykurt Sepet S, Gün Bozok H, Aydın ME. Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures. JNT. 2022(40):1-11.

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Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures
Journal of New Theory
https://doi.org/10.53570/jnt.1137525
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