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

Year 2016, Volume: 4 Issue: 1, 239 - 245, 01.04.2016

Günay Öztürk Betül Bulca Bengü K. Bayram Kadri Arslan

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.

Keywords

meridian surface Weingarten surface second fundamental form

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

Günay Öztürk Betül Bulca Bengü K. Bayram Kadri Arslan

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 Articles
Authors

Günay Öztürk

Betül Bulca

Bengü K. Bayram

Kadri Arslan

Publication Date April 1, 2016
Submission Date July 10, 2014
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.
AMA Öztürk G, Bulca B, Bayram BK, Arslan K. MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4. Konuralp J. Math. April 2016;4(1):239-245.
Chicago Öztürk, Günay, Betül Bulca, Bengü K. Bayram, and Kadri Arslan. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 239-45.
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 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, 2016.
ISNAD Öztürk, Günay et al. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4/1 (April 2016), 239-245.
JAMA 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, 2016, pp. 239-45.
Vancouver 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):239-45.
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