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A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map

Year 2021, Volume: 7 Issue: 2, 42 - 48, 09.12.2021

Abstract

In this study, we deal with the spherical product surface whose Gauss map G satisfies the equality L_1G=f(G+C) where L_1 is the Cheng-Yau operator in Galilean 3-space G_3 . We obtain the necessary and sufficient conditions for spherical product surface to have L_1-pointwise 1-type Gauss map in G_3.

References

  • [1] Alias LJ, Gürbüz N. An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures. Geom. Dedicata. 121, 2006, 113–127.
  • [2] Arslan K, Bayram BK, Bulca B, Kim YH, Murathan C, Öztürk G. Rotational embeddings in with pointwise 1-type Gauss map. Turk. J. Math. 35, 2011, 493–499.
  • [3] Arslan K, Bulca B, Bayram BK, Öztürk G, Ugail H. On spherical product surfaces in . International Conference on CyberWorlds. 1, 2009, 132–137.
  • [4] Arslan K, Bulca B, Milousheva V. Meridian surfaces in with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 51, 2014, 911–922.
  • [5] Aydın ME, Külahçı M, Öğrenmiş AO. Constant curvature translation surfaces in Galilean 3-space. International Electronic Journal of Geometry. 12, 2019, 9–19.
  • [6] Arslan K, Milousheva V. Meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space. Taiwanese Journal of Mathematics. 20, 2016, 311–332.
  • [7] Aydın ME, Öğrenmiş AO. Spherical product surfaces in the Galilean space. Konuralp Journal of Mathematics. 4, 2016, 290–298.
  • [8] Bulca B, Arslan K, Bayram BK, Öztürk G. Spherical product surfaces in . An. St. Univ. Ovidius Constanta. 20, 2012, 41–54.
  • [9] Chen BY. Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics. 1. World Scientific Publishing Co. Singapore, 1984.
  • [10] Chen BY. A report on submanifolds of finite type. Soochow J. Math. 22, 1996, 117–337.
  • [11] Chen BY. On submanifolds of finite type. Soochow J. Math. 9, 1983, 65–81.
  • [12] Chen BY, Piccinni P. Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35, 1987, 161–186.
  • [13] Chen BY, Choi M, Kim YH. Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. 42, 2005, 447–455.
  • [14] Cheng SY, Yau ST. Hypersurfaces with constant scalar curvature. Math. Ann. 225, 1977, 195–204.
  • [15] Choi M, Kim YH. Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38, 2001, 753–761.
  • [16] Güler E, Turgay NC. Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-space. Mediterr. J. Math. 16, 2019, 1–16. [17] Kashani SMB, On some -finite type (hyper)surfaces in . Bull. Korean Math. Soc. 46, 2009, 35–43.
  • [18] Kim DS, Kim JR, Kim YH. Cheng-Yau operator and Gauss map of surfaces of revolution. Bull. Malays. Math. Sci. Soc. 39, 2016, 1319–1327.
  • [19] Kim YH, Turgay NC. Surfaces in with -pointwise 1-type Gauss map. Bulletin of the Korean Mathematical Society. 50, 2013, 935–949.
  • [20] Kim YH, Turgay NC. On the ruled surfaces with -pointwise 1-type Gauss map. Kyungpook Math. J. 57, 2017, 133–144.
  • [21] Kişi , Öztürk G. A new type of tubular surface having pointwise 1-type Gauss map in Euclidean 4-space . J. Korean Math. Soc. 55, 2018, 923–938.
  • [22] Kişi , Öztürk G. Spherical product surface having pointwise 1-type Gauss map in Galilean 3-space . International Journal of Geometric Methods in Modern Physics. 16, 2019, 1–10.
  • [23] Kişi , Öztürk G. Tubular surface having pointwise 1-type Gauss map in Euclidean 4-space. International Electronic Journal of Geometry. 12, 2019, 202–209.
  • [24] Kuiper NH. Minimal total absolute curvature for immersions. Invent. Math. 10, 1970, 209–238.
  • [25] Mohammadpouri A. Hypersurfaces with -pointwise 1-type Gauss map. Journal of Mathematical Physics, Analysis, Geometry. 14, 2018, 67–77.
  • [26] Pavkovic BJ, Kamenarovic I. The equiform differential geometry of curves in the Galilean space . Glasnik Matematicki. 22, 1987, 449–457.
  • [27] Röschel O. Die Geometrie Des Galileischen Raumes. Forschungszentrum Graz Research Centre, Austria, 1986.
  • [28] Qian J, Kim YH. Classifications of canal surfaces with -pointwise 1-type Gauss map. Milan J. Math. 83, 2015, 145–155.
  • [29] Yaglom IM. A Simple Non-Euclidean Geometry and Its Physical Basis. Springer-Verlag Inc., New York, 1979.
  • [30] Yoon DW, Kim YH, Jung JS. Rotation surfaces with -pointwise 1-type Gauss map in pseudo-Galilean space. Annales Polonici Mathematici. 113, 2015, 255–267.
Year 2021, Volume: 7 Issue: 2, 42 - 48, 09.12.2021

Abstract

References

  • [1] Alias LJ, Gürbüz N. An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures. Geom. Dedicata. 121, 2006, 113–127.
  • [2] Arslan K, Bayram BK, Bulca B, Kim YH, Murathan C, Öztürk G. Rotational embeddings in with pointwise 1-type Gauss map. Turk. J. Math. 35, 2011, 493–499.
  • [3] Arslan K, Bulca B, Bayram BK, Öztürk G, Ugail H. On spherical product surfaces in . International Conference on CyberWorlds. 1, 2009, 132–137.
  • [4] Arslan K, Bulca B, Milousheva V. Meridian surfaces in with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 51, 2014, 911–922.
  • [5] Aydın ME, Külahçı M, Öğrenmiş AO. Constant curvature translation surfaces in Galilean 3-space. International Electronic Journal of Geometry. 12, 2019, 9–19.
  • [6] Arslan K, Milousheva V. Meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space. Taiwanese Journal of Mathematics. 20, 2016, 311–332.
  • [7] Aydın ME, Öğrenmiş AO. Spherical product surfaces in the Galilean space. Konuralp Journal of Mathematics. 4, 2016, 290–298.
  • [8] Bulca B, Arslan K, Bayram BK, Öztürk G. Spherical product surfaces in . An. St. Univ. Ovidius Constanta. 20, 2012, 41–54.
  • [9] Chen BY. Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics. 1. World Scientific Publishing Co. Singapore, 1984.
  • [10] Chen BY. A report on submanifolds of finite type. Soochow J. Math. 22, 1996, 117–337.
  • [11] Chen BY. On submanifolds of finite type. Soochow J. Math. 9, 1983, 65–81.
  • [12] Chen BY, Piccinni P. Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35, 1987, 161–186.
  • [13] Chen BY, Choi M, Kim YH. Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. 42, 2005, 447–455.
  • [14] Cheng SY, Yau ST. Hypersurfaces with constant scalar curvature. Math. Ann. 225, 1977, 195–204.
  • [15] Choi M, Kim YH. Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38, 2001, 753–761.
  • [16] Güler E, Turgay NC. Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-space. Mediterr. J. Math. 16, 2019, 1–16. [17] Kashani SMB, On some -finite type (hyper)surfaces in . Bull. Korean Math. Soc. 46, 2009, 35–43.
  • [18] Kim DS, Kim JR, Kim YH. Cheng-Yau operator and Gauss map of surfaces of revolution. Bull. Malays. Math. Sci. Soc. 39, 2016, 1319–1327.
  • [19] Kim YH, Turgay NC. Surfaces in with -pointwise 1-type Gauss map. Bulletin of the Korean Mathematical Society. 50, 2013, 935–949.
  • [20] Kim YH, Turgay NC. On the ruled surfaces with -pointwise 1-type Gauss map. Kyungpook Math. J. 57, 2017, 133–144.
  • [21] Kişi , Öztürk G. A new type of tubular surface having pointwise 1-type Gauss map in Euclidean 4-space . J. Korean Math. Soc. 55, 2018, 923–938.
  • [22] Kişi , Öztürk G. Spherical product surface having pointwise 1-type Gauss map in Galilean 3-space . International Journal of Geometric Methods in Modern Physics. 16, 2019, 1–10.
  • [23] Kişi , Öztürk G. Tubular surface having pointwise 1-type Gauss map in Euclidean 4-space. International Electronic Journal of Geometry. 12, 2019, 202–209.
  • [24] Kuiper NH. Minimal total absolute curvature for immersions. Invent. Math. 10, 1970, 209–238.
  • [25] Mohammadpouri A. Hypersurfaces with -pointwise 1-type Gauss map. Journal of Mathematical Physics, Analysis, Geometry. 14, 2018, 67–77.
  • [26] Pavkovic BJ, Kamenarovic I. The equiform differential geometry of curves in the Galilean space . Glasnik Matematicki. 22, 1987, 449–457.
  • [27] Röschel O. Die Geometrie Des Galileischen Raumes. Forschungszentrum Graz Research Centre, Austria, 1986.
  • [28] Qian J, Kim YH. Classifications of canal surfaces with -pointwise 1-type Gauss map. Milan J. Math. 83, 2015, 145–155.
  • [29] Yaglom IM. A Simple Non-Euclidean Geometry and Its Physical Basis. Springer-Verlag Inc., New York, 1979.
  • [30] Yoon DW, Kim YH, Jung JS. Rotation surfaces with -pointwise 1-type Gauss map in pseudo-Galilean space. Annales Polonici Mathematici. 113, 2015, 255–267.
There are 29 citations in total.

Details

Primary Language English
Journal Section makaleler
Authors

İlim Kişi 0000-0002-4785-8165

Günay Öztürk 0000-0002-1608-0354

Publication Date December 9, 2021
Published in Issue Year 2021 Volume: 7 Issue: 2

Cite

APA Kişi, İ., & Öztürk, G. (2021). A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science, 7(2), 42-48.
AMA Kişi İ, Öztürk G. A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science. December 2021;7(2):42-48.
Chicago Kişi, İlim, and Günay Öztürk. “A Note on Spherical Product Surface With L_1-Pointwise 1-Type Gauss Map”. Eastern Anatolian Journal of Science 7, no. 2 (December 2021): 42-48.
EndNote Kişi İ, Öztürk G (December 1, 2021) A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science 7 2 42–48.
IEEE İ. Kişi and G. Öztürk, “A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map”, Eastern Anatolian Journal of Science, vol. 7, no. 2, pp. 42–48, 2021.
ISNAD Kişi, İlim - Öztürk, Günay. “A Note on Spherical Product Surface With L_1-Pointwise 1-Type Gauss Map”. Eastern Anatolian Journal of Science 7/2 (December 2021), 42-48.
JAMA Kişi İ, Öztürk G. A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science. 2021;7:42–48.
MLA Kişi, İlim and Günay Öztürk. “A Note on Spherical Product Surface With L_1-Pointwise 1-Type Gauss Map”. Eastern Anatolian Journal of Science, vol. 7, no. 2, 2021, pp. 42-48.
Vancouver Kişi İ, Öztürk G. A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science. 2021;7(2):42-8.