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

Yıl 2016, Cilt: 4 Sayı: 1, 239 - 245, 01.04.2016

Öz

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.

Kaynakça

  • [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.
Yıl 2016, Cilt: 4 Sayı: 1, 239 - 245, 01.04.2016

Öz

Kaynakça

  • [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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Günay Öztürk

Betül Bulca

Bengü K. Bayram

Kadri Arslan

Yayımlanma Tarihi 1 Nisan 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

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. Nisan 2016;4(1):239-245.
Chicago Öztürk, Günay, Betül Bulca, Bengü K. Bayram, ve Kadri Arslan. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 239-45.
EndNote Öztürk G, Bulca B, Bayram BK, Arslan K (01 Nisan 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, ve K. Arslan, “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”, Konuralp J. Math., c. 4, sy. 1, ss. 239–245, 2016.
ISNAD Öztürk, Günay vd. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics 4/1 (Nisan 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 vd. “MERIDIAN SURFACES OF WEINGARTEN TYPE IN 4-DIMENSIONAL EUCLIDEAN SPACE E4”. Konuralp Journal of Mathematics, c. 4, sy. 1, 2016, ss. 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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