HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Title & Authors
HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Choi, Mie-Kyung; Kim, Dong-Soo; Kim, Young-Ho;

Abstract
The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1-type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine helicoidal surface of polynomial kind with pointwise 1-type Gauss map of the first kind and a right cone is the only rational helicoidal surface with pointwise 1-type Gauss map of the second kind. Also, we give a characterization of rational helicoidal surface with harmonic or pointwise 1-type Gauss map.
Keywords
helicoidal surfaces;helicoid;right cone;pointwise 1-type Gauss map;
Language
English
Cited by
1.
HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE II,;;;

대한수학회보, 2009. vol.46. 3, pp.567-576
2.
SURFACES OF REVOLUTION SATISFYING ΔIIG = f(G + C),;;

대한수학회보, 2013. vol.50. 4, pp.1061-1067
3.
CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP,;;

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

대한수학회보, 2014. vol.51. 6, pp.1863-1874
5.
ON SPACELIKE ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP,;

대한수학회보, 2015. vol.52. 1, pp.301-312
6.
SHAPE OPERATOR AND GAUSS MAP OF POINTWISE 1-TYPE,;;

대한수학회지, 2015. vol.52. 6, pp.1337-1346
1.
Helicoidal surfaces satisfying $${\Delta ^{II}\mathbf{G}=f(\mathbf{G}+C)}$$ Δ II G = f ( G + C ), Journal of Geometry, 2016, 107, 3, 523
2.
SHAPE OPERATOR AND GAUSS MAP OF POINTWISE 1-TYPE, Journal of the Korean Mathematical Society, 2015, 52, 6, 1337
3.
General rotational surfaces with pointwise 1-type Gauss map in pseudo-Euclidean space E 2 4, Indian Journal of Pure and Applied Mathematics, 2015, 46, 1, 107
4.
ON SPACELIKE ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 301
5.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E4, Honam Mathematical Journal, 2016, 38, 2, 305
6.
BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E41, Bulletin of the Korean Mathematical Society, 2014, 51, 6, 1863
7.
SURFACES OF REVOLUTION SATISFYING ΔIIG = f(G + C), Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1061
8.
CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1345
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