Research Article
BibTex RIS Cite

MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4

Year 2016, Volume: 4 Issue: 1, 239 - 245, 01.04.2016
https://izlik.org/JA96MY45SZ

Abstract

In this paper, we study meridian surfaces of Weingarten type in Euclidean 4-space E4. We give the necessary and sucient conditions for a meridian surface in E4 to become Weingarten type.

References

  • [1] K. Arslan and V. Milousheva, Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise 1-type Gauss map in Minkowski 4-Space, accepted Taiwanese Journal of Mathematics.
  • [2] B. Bulca, K. Arslan and V. Milousheva, Meridian Surfaces in E4 with Pointwise 1-type Gauss Map, Bull. Korean Math. Soc., 51 (2014), 911{922.
  • [3] B. Y. Chen, Geometry of Submanifolds , Dekker, New York, 1973.
  • [4] B. Y. Chen, Pseudo-umbilical surfaces with constant Gauss curvature, Proceedings of the Edinburgh Mathematical Society (Series 2), 18(2) (1972), 143-148.
  • [5] F. Dillen and W. Kuhnel, Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98 (1999), 307-320.
  • [6] J. A. Galvez, A. Martinez and F. Milan, Linear Weingarten Surfaces in R3, Monatsh. Math., 138 (2003), 133-144.
  • [7] G. Ganchev and V. Milousheva, Invariants and Bonnet-type theorem for surfaces in R4, Cent. Eur. J. Math., 8(6) (2010) 993-1008.
  • [8] G. Ganchev and V. Milousheva, Special Class of Meridian Surfaces in the Four-Dimensional Euclidean Space, arXiv: 1402.5848v1 [math.DG], 24 Feb. 2014.
  • [9] G. Ganchev and V. Milousheva, Geometric Interpretation of the Invariants of a Surface in R4 via Tangent Indicatrix and the Normal Curvature Ellipse, arXiv:0905.4453v1 [math.DG], 27 May 2009.
  • [10] W. Kuhnel and M. Steller, On Closed Weingarten Surfaces, Monatsh. Math., 146 (2005), 113-126.
  • [11] Y. H. Kim and D. W. Yoon, Classi cation of ruled surfaces in Minkowski 3-spaces, J. Geom. Phys., 49 (2004), 89-100.
  • [12] W. Kuhnel, Ruled W-surfaces, Arch. Math., 62 (1994), 475-480.
  • [13] R. Lopez, On linear Weingarten surfaces, International J. Math., 19 (2008), 439-448.
  • [14] R. Lopez, Special Weingarten surfaces foliated by circles, Monatsh. Math., 154 (2008), 289- 302.
  • [15] M. I. Munteanu and A. I. Nistor, Polynomial translationWeingarten surfaces in 3-dimensional Euclidean space, arXiv:0809.4745v1 [math.DG], 27 Sep 2008.
  • [16] J. Weingarten, Ueber eine Klasse auf einander abwickelbarer Flaachen, J. Reine Angew. Math. 59 (1861), 382{393.
  • [17] J. Weingarten, Ueber die Flachen, derer Normalen eine gegebene Flache beruhren, J. Reine Angew. Math. 62 (1863), 61-63.
  • [18] D. W. Yoon, Some properties of the helicoid as ruled surfaces, JP Jour. Geom. Topology, 2 (2002), 141-147.
  • [19] D. W. Yoon, Polynomial translation surfaces of Weingarten types in Euclidean 3-space, Cent. Eur. J. Math., 8(3) (2010), 430-436.

Year 2016, Volume: 4 Issue: 1, 239 - 245, 01.04.2016
https://izlik.org/JA96MY45SZ

Abstract

References

  • [1] K. Arslan and V. Milousheva, Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise 1-type Gauss map in Minkowski 4-Space, accepted Taiwanese Journal of Mathematics.
  • [2] B. Bulca, K. Arslan and V. Milousheva, Meridian Surfaces in E4 with Pointwise 1-type Gauss Map, Bull. Korean Math. Soc., 51 (2014), 911{922.
  • [3] B. Y. Chen, Geometry of Submanifolds , Dekker, New York, 1973.
  • [4] B. Y. Chen, Pseudo-umbilical surfaces with constant Gauss curvature, Proceedings of the Edinburgh Mathematical Society (Series 2), 18(2) (1972), 143-148.
  • [5] F. Dillen and W. Kuhnel, Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98 (1999), 307-320.
  • [6] J. A. Galvez, A. Martinez and F. Milan, Linear Weingarten Surfaces in R3, Monatsh. Math., 138 (2003), 133-144.
  • [7] G. Ganchev and V. Milousheva, Invariants and Bonnet-type theorem for surfaces in R4, Cent. Eur. J. Math., 8(6) (2010) 993-1008.
  • [8] G. Ganchev and V. Milousheva, Special Class of Meridian Surfaces in the Four-Dimensional Euclidean Space, arXiv: 1402.5848v1 [math.DG], 24 Feb. 2014.
  • [9] G. Ganchev and V. Milousheva, Geometric Interpretation of the Invariants of a Surface in R4 via Tangent Indicatrix and the Normal Curvature Ellipse, arXiv:0905.4453v1 [math.DG], 27 May 2009.
  • [10] W. Kuhnel and M. Steller, On Closed Weingarten Surfaces, Monatsh. Math., 146 (2005), 113-126.
  • [11] Y. H. Kim and D. W. Yoon, Classi cation of ruled surfaces in Minkowski 3-spaces, J. Geom. Phys., 49 (2004), 89-100.
  • [12] W. Kuhnel, Ruled W-surfaces, Arch. Math., 62 (1994), 475-480.
  • [13] R. Lopez, On linear Weingarten surfaces, International J. Math., 19 (2008), 439-448.
  • [14] R. Lopez, Special Weingarten surfaces foliated by circles, Monatsh. Math., 154 (2008), 289- 302.
  • [15] M. I. Munteanu and A. I. Nistor, Polynomial translationWeingarten surfaces in 3-dimensional Euclidean space, arXiv:0809.4745v1 [math.DG], 27 Sep 2008.
  • [16] J. Weingarten, Ueber eine Klasse auf einander abwickelbarer Flaachen, J. Reine Angew. Math. 59 (1861), 382{393.
  • [17] J. Weingarten, Ueber die Flachen, derer Normalen eine gegebene Flache beruhren, J. Reine Angew. Math. 62 (1863), 61-63.
  • [18] D. W. Yoon, Some properties of the helicoid as ruled surfaces, JP Jour. Geom. Topology, 2 (2002), 141-147.
  • [19] D. W. Yoon, Polynomial translation surfaces of Weingarten types in Euclidean 3-space, Cent. Eur. J. Math., 8(3) (2010), 430-436.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Günay Öztürk

Betül Bulca

Bengü K. Bayram

Kadri Arslan

Submission Date July 10, 2014
Publication Date April 1, 2016
IZ https://izlik.org/JA96MY45SZ
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Öztürk, G., Bulca, B., Bayram, B. K., & Arslan, K. (2016). MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp Journal of Mathematics, 4(1), 239-245. https://izlik.org/JA96MY45SZ
AMA 1.Öztürk G, Bulca B, Bayram BK, Arslan K. MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp J. Math. 2016;4(1):239-245. https://izlik.org/JA96MY45SZ
Chicago Öztürk, Günay, Betül Bulca, Bengü K. Bayram, and Kadri Arslan. 2016. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4 (1): 239-45. https://izlik.org/JA96MY45SZ.
EndNote Öztürk G, Bulca B, Bayram BK, Arslan K (April 1, 2016) MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp Journal of Mathematics 4 1 239–245.
IEEE [1]G. Öztürk, B. Bulca, B. K. Bayram, and K. Arslan, “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”, Konuralp J. Math., vol. 4, no. 1, pp. 239–245, Apr. 2016, [Online]. Available: https://izlik.org/JA96MY45SZ
ISNAD Öztürk, Günay - Bulca, Betül - Bayram, Bengü K. - Arslan, Kadri. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4/1 (April 1, 2016): 239-245. https://izlik.org/JA96MY45SZ.
JAMA 1.Öztürk G, Bulca B, Bayram BK, Arslan K. MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp J. Math. 2016;4:239–245.
MLA Öztürk, Günay, et al. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics, vol. 4, no. 1, Apr. 2016, pp. 239-45, https://izlik.org/JA96MY45SZ.
Vancouver 1.Günay Öztürk, Betül Bulca, Bengü K. Bayram, Kadri Arslan. MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp J. Math. [Internet]. 2016 Apr. 1;4(1):239-45. Available from: https://izlik.org/JA96MY45SZ
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.