SavedAdd your journal

Journals / Eastern Anatolian Journal of Science / 2021 / Volume: 7 Issue: 2

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

İlim Kişi(KOCAELİ ÜNİVERSİTESİ)0000-0002-4785-8165
Günay Öztürk(IZMIR DEMOCRACY UNIVERSITY)0000-0002-1608-0354
Pages
—
Publication Date
2021-12-09
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We obtain the necessary and sufficient conditions for spherical product surface to have L_1-pointwise 1-type Gauss map in G_3.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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 .
📊
Key Findings & Data: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 .
💡
Conclusion & Impact:We obtain the necessary and sufficient conditions for spherical product surface to have L_1-pointwise 1-type Gauss map in G_3.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Spherical product surface · Cheng-Yau operator · Galilean 3-space

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.

🔖

Cite This Article

Kişi, İ., Öztürk, G. (2021). A Note on Spherical Product Surface with L_1-Pointwise 1-Type Gauss Map. Eastern Anatolian Journal of Science, Volume: 7 Issue: 2. https://ajindex.com/articles/1475657

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (36)

  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.
  17. 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.
  18. Kim YH, Turgay NC. Surfaces in with -pointwise 1-type Gauss map. Bulletin of the Korean Mathematical Society. 50, 2013, 935–949.
  19. Kim YH, Turgay NC. On the ruled surfaces with -pointwise 1-type Gauss map. Kyungpook Math. J. 57, 2017, 133–144.
  20. 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.
  21. 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.
  22. Kişi, Öztürk G. Tubular surface having pointwise 1-type Gauss map in Euclidean 4-space. International Electronic Journal of Geometry. 12, 2019, 202–209.
  23. Kuiper NH. Minimal total absolute curvature for immersions. Invent. Math. 10, 1970, 209–238.
  24. Mohammadpouri A. Hypersurfaces with -pointwise 1-type Gauss map. Journal of Mathematical Physics, Analysis, Geometry. 14, 2018, 67–77.
  25. Pavkovic BJ, Kamenarovic I. The equiform differential geometry of curves in the Galilean space. Glasnik Matematicki. 22, 1987, 449–457.
  26. Röschel O. Die Geometrie Des Galileischen Raumes. Forschungszentrum Graz Research Centre, Austria, 1986.
  27. Qian J, Kim YH. Classifications of canal surfaces with -pointwise 1-type Gauss map. Milan J. Math. 83, 2015, 145–155.
  28. Yaglom IM. A Simple Non-Euclidean Geometry and Its Physical Basis. Springer-Verlag Inc., New York, 1979.
  29. 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.
  30. Arslan K, Bulca B, Bayram BK, Öztürk G, Ugail H. On spherical product surfaces in. International Conference on CyberWorlds. 1, 2009, 132–137.
  31. Bulca B, Arslan K, Bayram BK, Öztürk G. Spherical product surfaces in. An. St. Univ. Ovidius Constanta. 20, 2012, 41–54.
  32. 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.
  33. 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.
  34. 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.
  35. Kişi, Öztürk G. Tubular surface having pointwise 1-type Gauss map in Euclidean 4-space. International Electronic Journal of Geometry. 12, 2019, 202–209.
  36. Pavkovic BJ, Kamenarovic I. The equiform differential geometry of curves in the Galilean space. Glasnik Matematicki. 22, 1987, 449–457.