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Öklid-3 uzayındaki tzitzeica yüzeyleri üzerine

Year 2021, Volume: 23 Issue: 1, 277 - 290, 29.01.2021

Bengü Bayram Emrah Tunç

https://doi.org/10.25092/baunfbed.850807
Cited By: 1

Abstract

Bu çalışmada Öklid-3 uzayındaki Tzitzeica yüzeylerini incelendi. Bazı yüzeylerin Tzitzeica yüzey şartları incelendi. Son olarak bu yüzeyler için örnekler verildi.

Keywords

Tzitzeica şartı Tzitzeica yüzeyi temel form Gauss eğriliği

References

  • Bobe, A., Boskoff, W.G. and Ciuca, M.G., Tzitzeica type centro-affine invariants in Minkowski space, Analele Stiintifice ale Universitatii Ovidius Constanta, 20(2), 27-34, (2012).
  • Crasmareanu, M., Cylindrical Tzitzeica curves implies forced harmonic oscillators, Balkan Journal of Geometry and Its Applications, 7(1), 37-42, (2002).
  • Vilcu, G.E., A geometric perspective on the generalized Cobb-Douglas production function, Applied Mathematics Letters, 24, 777-783, (2011).
  • Constantinescu, O., Crasmareanu, M., A new Tzitzeica hypersurface and cubic Finslerian metrics of Berwall type, Balkan Journal of Geometry and Its Applications, 16(2), 27-34, (2011).
  • O’neill, B., Elemantary Differential Geometry, (1966).
  • Sipus, Z.M., Divjak, B., Translation surface in the Galilean space, Glasnik Matematicki. Serija III, 46(2), 455–469, (2011).
  • Bekkar, M., Senoussi, B., Factorable surfaces in the 3-Dimensional Lorentz-Minkowski space satisfying ∆II ri=λiri, International Journal of Geometry, 103, 17-29, (2012).
  • Meng, H., and Liu, H., Factorable surfaces in Minkowski 3-space, Bulletin of the Korean Mathematical Society, 155-169, (2009).
  • Turhan, E., Altay, G., Maximal and minimal surfaces of factorable surfaces in Heis3, International Journal of Open Problems in Computer Science and Mathematics, 3(2), (2010).
  • Yu, Y., and Liu, H., The factorable minimal surfaces, Proceedings of the Eleventh International Workshop on Differential Geometry, 33-39, Kyungpook Nat. Univ., Taegu, (2007).
  • Jaklic, A., Leonardis, A., Solina, F., Segmentation and recovery of superquadrics, Kluver Academic Publishers, 20, (2000).
  • Bulca, B., Arslan, K., (Kılıc) Bayram, B., Ozturk, G. and Ugail, H., On spherical product surfaces in E3, IEEE Computer Society, Int. Conference on Cyberworlds, (2009).

On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$

Year 2021, Volume: 23 Issue: 1, 277 - 290, 29.01.2021

Bengü Bayram Emrah Tunç

https://doi.org/10.25092/baunfbed.850807
Cited By: 1

Abstract

In this study, we consider Tzitzeica surfaces (Tz-surface) in Euclidean 3-Space $\mathbb{E}^3$. We have been obtained Tzitzeica surfaces conditions of some surfaces. Finally, examples are given for these surfaces.

Keywords

Tzitzeica condition Tzitzeica surface fundamental form Gauss curvature

References

  • Bobe, A., Boskoff, W.G. and Ciuca, M.G., Tzitzeica type centro-affine invariants in Minkowski space, Analele Stiintifice ale Universitatii Ovidius Constanta, 20(2), 27-34, (2012).
  • Crasmareanu, M., Cylindrical Tzitzeica curves implies forced harmonic oscillators, Balkan Journal of Geometry and Its Applications, 7(1), 37-42, (2002).
  • Vilcu, G.E., A geometric perspective on the generalized Cobb-Douglas production function, Applied Mathematics Letters, 24, 777-783, (2011).
  • Constantinescu, O., Crasmareanu, M., A new Tzitzeica hypersurface and cubic Finslerian metrics of Berwall type, Balkan Journal of Geometry and Its Applications, 16(2), 27-34, (2011).
  • O’neill, B., Elemantary Differential Geometry, (1966).
  • Sipus, Z.M., Divjak, B., Translation surface in the Galilean space, Glasnik Matematicki. Serija III, 46(2), 455–469, (2011).
  • Bekkar, M., Senoussi, B., Factorable surfaces in the 3-Dimensional Lorentz-Minkowski space satisfying ∆II ri=λiri, International Journal of Geometry, 103, 17-29, (2012).
  • Meng, H., and Liu, H., Factorable surfaces in Minkowski 3-space, Bulletin of the Korean Mathematical Society, 155-169, (2009).
  • Turhan, E., Altay, G., Maximal and minimal surfaces of factorable surfaces in Heis3, International Journal of Open Problems in Computer Science and Mathematics, 3(2), (2010).
  • Yu, Y., and Liu, H., The factorable minimal surfaces, Proceedings of the Eleventh International Workshop on Differential Geometry, 33-39, Kyungpook Nat. Univ., Taegu, (2007).
  • Jaklic, A., Leonardis, A., Solina, F., Segmentation and recovery of superquadrics, Kluver Academic Publishers, 20, (2000).
  • Bulca, B., Arslan, K., (Kılıc) Bayram, B., Ozturk, G. and Ugail, H., On spherical product surfaces in E3, IEEE Computer Society, Int. Conference on Cyberworlds, (2009).
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Bengü Bayram This is me 0000-0002-1237-5892

Emrah Tunç This is me 0000-0002-7630-0996

Publication Date January 29, 2021
Submission Date May 21, 2020
Published in Issue Year 2021 Volume: 23 Issue: 1

Cite

APA Bayram, B., & Tunç, E. (2021). On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(1), 277-290. https://doi.org/10.25092/baunfbed.850807
AMA Bayram B, Tunç E. On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$. BAUN Fen. Bil. Enst. Dergisi. January 2021;23(1):277-290. doi:10.25092/baunfbed.850807
Chicago Bayram, Bengü, and Emrah Tunç. “On Tzitzeica Surfaces in Euclidean 3-Space $\mathbb{E}^3$”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23, no. 1 (January 2021): 277-90. https://doi.org/10.25092/baunfbed.850807.
EndNote Bayram B, Tunç E (January 1, 2021) On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23 1 277–290.
IEEE B. Bayram and E. Tunç, “On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$”, BAUN Fen. Bil. Enst. Dergisi, vol. 23, no. 1, pp. 277–290, 2021, doi: 10.25092/baunfbed.850807.
ISNAD Bayram, Bengü - Tunç, Emrah. “On Tzitzeica Surfaces in Euclidean 3-Space $\mathbb{E}^3$”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23/1 (January 2021), 277-290. https://doi.org/10.25092/baunfbed.850807.
JAMA Bayram B, Tunç E. On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$. BAUN Fen. Bil. Enst. Dergisi. 2021;23:277–290.
MLA Bayram, Bengü and Emrah Tunç. “On Tzitzeica Surfaces in Euclidean 3-Space $\mathbb{E}^3$”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 23, no. 1, 2021, pp. 277-90, doi:10.25092/baunfbed.850807.
Vancouver Bayram B, Tunç E. On tzitzeica surfaces in euclidean 3-space $\mathbb{E}^3$. BAUN Fen. Bil. Enst. Dergisi. 2021;23(1):277-90.

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