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

Yıl 2016, Cilt: 9 Sayı: 2, 21 - 26, 30.10.2016
https://doi.org/10.36890/iejg.584575

Öz

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

Kaynakça

  • [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.
Yıl 2016, Cilt: 9 Sayı: 2, 21 - 26, 30.10.2016
https://doi.org/10.36890/iejg.584575

Öz

Kaynakça

  • [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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Mehmet Yıldırım

Yayımlanma Tarihi 30 Ekim 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 2

Kaynak Göster

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. Ekim 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, sy. 2 (Ekim 2016): 21-26. https://doi.org/10.36890/iejg.584575.
EndNote Yıldırım M (01 Ekim 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., c. 9, sy. 2, ss. 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 (Ekim 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, c. 9, sy. 2, 2016, ss. 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.