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.
[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, Classication 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
[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, Classication 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.
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.