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CLASSIFICATIONS OF ROTATION SURFACES IN PSEUDO-EUCLIDEAN SPACE
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 Title & Authors
CLASSIFICATIONS OF ROTATION SURFACES IN PSEUDO-EUCLIDEAN SPACE
Kim, Young-Ho; Yoon, Dae-Won;
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 Abstract
In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.
 Keywords
rotation surfaces;Gauss map;finite type;Pseudo-Euclidean space.;
 Language
English
 Cited by
1.
ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS,;;;

대한수학회보, 2009. vol.46. 6, pp.1141-1149 crossref(new window)
2.
CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP,;;

대한수학회보, 2013. vol.50. 4, pp.1345-1356 crossref(new window)
3.
BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E41,;;

대한수학회보, 2014. vol.51. 6, pp.1863-1874 crossref(new window)
1.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E4, Honam Mathematical Journal, 2016, 38, 2, 305  crossref(new windwow)
2.
BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E41, Bulletin of the Korean Mathematical Society, 2014, 51, 6, 1863  crossref(new windwow)
3.
Quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map in pseudo-Euclidean 4-space, Journal of Geometry and Physics, 2016, 106, 171  crossref(new windwow)
4.
Spacelike Rotational Surfaces of Elliptic, Hyperbolic and Parabolic Types in Minkowski Space E 1 4 ${E^{4}_{1}}$ with Pointwise 1-Type Gauss Map, Mathematical Physics, Analysis and Geometry, 2014, 17, 1-2, 247  crossref(new windwow)
5.
ON SPACELIKE ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 301  crossref(new windwow)
6.
Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map, Results in Mathematics, 2016  crossref(new windwow)
7.
CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1345  crossref(new windwow)
8.
Homothetic Motions and Lie Groups In, Journal of Dynamical Systems and Geometric Theories, 2013, 11, 1-2, 23  crossref(new windwow)
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