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On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map

Year 2016, , 21 - 26, 30.10.2016
https://doi.org/10.36890/iejg.584575

Abstract

In this article, we study the tensor product surfaces of two Lorentzian planar, non-null curves to have pointwise 1-type Gauss map.

References

  • [1] Arslan, K., Bayram, B. K., Bulca, B., Kim, Y. H., Murathan, C. and Ozturk, G., Rotational embeddings in E4 with pointwise 1-type Gaussmap. Turk. J. Math. 35 (2011), 493-499.
  • [2] Arslan, K., Bulca, B., Kılıc, B., Kim, Y. H., Murathan, C. and Ozturk, G., Tensor Product Surfaces with Pointwise 1-Type Gauss Map. Bull.Korean Math. Soc. 48 (2011), 601-609.
  • [3] Arslan, K. and Murathan, C., Tensor product surfaces of pseudo-Euclidean planar curves. Geometry and topology of submanifolds, VII (Leuven, 1994/Brussels, 1994) World Sci. Publ., River Edge, NJ (1995), 71-74.
  • [4] Carmo, M. do, Riemannian geometry. Birkhauser, 1993.
  • [5] Chen, B. Y., Choi, M. and Kim, Y. H. , Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. 42 (2005), 447-455.
  • [6] Chen, B. Y., Geometry of Submanifolds. M. Dekker, New York, 1973.
  • [7] Chen, B. Y., Differential Geometry of semiring of immersions, I: General Theory. Bull. Inst. Math. Acad. Sinica 21 (1993), 1-34.
  • [8] Choi, M. and Kim, Y. H., Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38(2001), 753–761.
  • [9] Decruyenaere, F., Dillen, F., Verstraelen, L. and Vrancken, L., The semiring of immersions of manifolds. Beitrage Algebra Geom. 34 (1993), 209-215.
  • [10] Decruyenaere, F., Dillen, F., Mihai, I. and Verstraelen, L., Tensor products of spherical and equivariant immersions. Bull. Belg. Math. Soc.- Simon Stevin 1 (1994), 643-648.
  • [11] Dursun, U. and Arsan, G.G., Surfaces in the Euclidean space E4 with pointwise 1-type Gauss map. Hacet. J. Math. Stat. 40 (2011), 617-625.
  • [12] İlarslan, K. and Nesovic, E., Tensor product surfaces of a Lorentzian space curve and a Lorentzian plane curve. Bull. Inst. Math. Acad. Sinica 33 (2005), 151-171.
  • [13] Kim, Y.H. and Yoon, D. W., Ruled surfaces with pointwise 1-type Gauss map. J. Geom. Phys. 34 (2000), 191-205.
  • [14] Kim, Y.H. and Yoon, D. W., Classification of rotation surfaces in pseudo-Euclidean space. J. Korean Math. 41 (2004), 379-396.
  • [15] Niang, A., Rotation surfaces with 1-type Gauss map, Bull. Korean Math. Soc. 42 (2005), 23-27.
  • [16] O‘Neill, B., Semi - Riemannian Geometry with applications to relavity. Academic Press. New York, (1983).
  • [17] Özkaldı, S. and Yaylı, Y., Tensor product surfaces in R4 and Lie groups. Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 69-77.
  • [18] Yoon, D. W., On the Gauss map of translation surfaces in Minkowski 3-spaces. Taiwanese J. Math. 6 (2002), 389-398.
Year 2016, , 21 - 26, 30.10.2016
https://doi.org/10.36890/iejg.584575

Abstract

References

  • [1] Arslan, K., Bayram, B. K., Bulca, B., Kim, Y. H., Murathan, C. and Ozturk, G., Rotational embeddings in E4 with pointwise 1-type Gaussmap. Turk. J. Math. 35 (2011), 493-499.
  • [2] Arslan, K., Bulca, B., Kılıc, B., Kim, Y. H., Murathan, C. and Ozturk, G., Tensor Product Surfaces with Pointwise 1-Type Gauss Map. Bull.Korean Math. Soc. 48 (2011), 601-609.
  • [3] Arslan, K. and Murathan, C., Tensor product surfaces of pseudo-Euclidean planar curves. Geometry and topology of submanifolds, VII (Leuven, 1994/Brussels, 1994) World Sci. Publ., River Edge, NJ (1995), 71-74.
  • [4] Carmo, M. do, Riemannian geometry. Birkhauser, 1993.
  • [5] Chen, B. Y., Choi, M. and Kim, Y. H. , Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. 42 (2005), 447-455.
  • [6] Chen, B. Y., Geometry of Submanifolds. M. Dekker, New York, 1973.
  • [7] Chen, B. Y., Differential Geometry of semiring of immersions, I: General Theory. Bull. Inst. Math. Acad. Sinica 21 (1993), 1-34.
  • [8] Choi, M. and Kim, Y. H., Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38(2001), 753–761.
  • [9] Decruyenaere, F., Dillen, F., Verstraelen, L. and Vrancken, L., The semiring of immersions of manifolds. Beitrage Algebra Geom. 34 (1993), 209-215.
  • [10] Decruyenaere, F., Dillen, F., Mihai, I. and Verstraelen, L., Tensor products of spherical and equivariant immersions. Bull. Belg. Math. Soc.- Simon Stevin 1 (1994), 643-648.
  • [11] Dursun, U. and Arsan, G.G., Surfaces in the Euclidean space E4 with pointwise 1-type Gauss map. Hacet. J. Math. Stat. 40 (2011), 617-625.
  • [12] İlarslan, K. and Nesovic, E., Tensor product surfaces of a Lorentzian space curve and a Lorentzian plane curve. Bull. Inst. Math. Acad. Sinica 33 (2005), 151-171.
  • [13] Kim, Y.H. and Yoon, D. W., Ruled surfaces with pointwise 1-type Gauss map. J. Geom. Phys. 34 (2000), 191-205.
  • [14] Kim, Y.H. and Yoon, D. W., Classification of rotation surfaces in pseudo-Euclidean space. J. Korean Math. 41 (2004), 379-396.
  • [15] Niang, A., Rotation surfaces with 1-type Gauss map, Bull. Korean Math. Soc. 42 (2005), 23-27.
  • [16] O‘Neill, B., Semi - Riemannian Geometry with applications to relavity. Academic Press. New York, (1983).
  • [17] Özkaldı, S. and Yaylı, Y., Tensor product surfaces in R4 and Lie groups. Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 69-77.
  • [18] Yoon, D. W., On the Gauss map of translation surfaces in Minkowski 3-spaces. Taiwanese J. Math. 6 (2002), 389-398.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mehmet Yıldırım

Publication Date October 30, 2016
Published in Issue Year 2016

Cite

APA Yıldırım, M. (2016). On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map. International Electronic Journal of Geometry, 9(2), 21-26. https://doi.org/10.36890/iejg.584575
AMA Yıldırım M. On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map. Int. Electron. J. Geom. October 2016;9(2):21-26. doi:10.36890/iejg.584575
Chicago Yıldırım, Mehmet. “On Tensor Product Surfaces of Lorentzian Planar Curves With Pointwise 1-Type Gauss Map”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 21-26. https://doi.org/10.36890/iejg.584575.
EndNote Yıldırım M (October 1, 2016) On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map. International Electronic Journal of Geometry 9 2 21–26.
IEEE M. Yıldırım, “On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 21–26, 2016, doi: 10.36890/iejg.584575.
ISNAD Yıldırım, Mehmet. “On Tensor Product Surfaces of Lorentzian Planar Curves With Pointwise 1-Type Gauss Map”. International Electronic Journal of Geometry 9/2 (October 2016), 21-26. https://doi.org/10.36890/iejg.584575.
JAMA Yıldırım M. On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map. Int. Electron. J. Geom. 2016;9:21–26.
MLA Yıldırım, Mehmet. “On Tensor Product Surfaces of Lorentzian Planar Curves With Pointwise 1-Type Gauss Map”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 21-26, doi:10.36890/iejg.584575.
Vancouver Yıldırım M. On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map. Int. Electron. J. Geom. 2016;9(2):21-6.