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SOME PROPERTIES OF PARALLEL SURFACES IN EUCLIDEAN 3-SPACES
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  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 4,  2008, pp.637-644
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.4.637
 Title & Authors
SOME PROPERTIES OF PARALLEL SURFACES IN EUCLIDEAN 3-SPACES
Yoon, Dae-Won;
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 Abstract
In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.
 Keywords
Gaussian curvature;mean curvature;ruled surface;parallel surface;Weingarten surface;linear Weingarten surface;
 Language
English
 Cited by
 References
1.
D.E. Blair and Th. Koufogiorgos, Ruled surfaces with vanishing second Gaussian curvature, Monatsh. Math. 113 (1992) 177-181 crossref(new window)

2.
F. Dillen and W. Sodsiri, Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom. 83 (2005) 10-21 crossref(new window)

3.
J.A. Galvez, A. Martinez and F. Milan, Linear Weingarten surfaces in $\mathbb{R}^3$, Monatsh. Math. 138 (2003) 133-144 crossref(new window)

4.
Y.H. Kim and D.W. Yoon, Classification of ruled surfaces in Minkowski 3-spaces, J. Geom. Physics 49 (2001) 89-100

5.
Y.H. Kim and D.W. Yoon, On non-developable ruled surfaces in Lorentz-Minkowski 3-spaces, Taiwanccs J. Math. 11 (2007) 197-214

6.
N.G.Kim and D.W. Yoon, Mean curvature of non-degenerate second fundamental form of ruled surfaces, Honam Math. J. 28 (2006) 549-558

7.
W. Kuhnel, Ruled W-surfaces, Arch. Math. 62 (1991),475-480

8.
R. Lopez, Rotational linear Weingarten surfaces of hyperbolic type, to appear in Israel J.Math.

9.
R. Lopez, Special Weingarten surfaces foliated by circles, to appear in Monatsh. Math.

10.
K.-R. Park and G.-I Kim, Offsets of ruled surfaces, J. Korea Computer Graphics Society 4 (1998) 69-75

11.
A. Pressley, Elementary differential geometry, Springer (2002)

12.
J.A.A. Sanchez and J. M. Espinar, Hyperbolic linear Weingarten surfaces in $\mathbb{R}^3$, Bull. Braz. Math. Soc. New Series 38 (2007) 291-300 crossref(new window)

13.
G. Stamou, Regelflachen vom Weingarten-type, Colloq. Math. 79 (1999) 77-84

14.
D.W. Yoon, Some properties of the helicoid all ruled surfaces, JP Jour. Geom. Topology 2 (2002) 141-147

15.
D.W. Yoon, On non-developable ruled surfaces in Euclidean 3-spaces, Indian J. pure appl. Math. 38 (2007) 281-289

16.
D.F. Zuo. Time-like linear Weingarten surfaces in Lorentz spaces forms, Acta Math. Sinica. English Series 22 (2005) 1-6