Tubes in the Euclidean 3-space with coordinate finite type Gauss map

2021 ◽  
Author(s):  
Hassan Al-Zoubi ◽  
Tareq Hamadneh ◽  
Hamza Alzaareer ◽  
Mutaz Al-Sabbagh
Keyword(s):  
Finite Type ◽  
Gauss Map

Ruled submanifolds with finite type Gauss map

1994 ◽  
Vol 49 (1-2) ◽  
pp. 42-45 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Finite Type ◽  
Gauss Map

scholarly journals Ruled Surfaces and Tubes with Finite Type Gauss Map

1993 ◽  
Vol 16 (2) ◽  
pp. 341-349 ◽  
Author(s):  
Christos BAIKOUSSIS ◽  
Bang-yen CHEN ◽  
Leopold VERSTRAELEN
Keyword(s):  
Finite Type ◽  
Gauss Map ◽  
Ruled Surfaces

Hyperbolic submanifolds with finite type hyperbolic Gauss map

2015 ◽  
Vol 26 (02) ◽  
pp. 1550014 ◽  
Author(s):  
Uğur Dursun ◽  
Rüya Yeğin
Keyword(s):  
Scalar Curvature ◽  
Finite Type ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Gauss Map ◽  
Hyperbolic Spaces ◽  
Nonzero Constant ◽  
Hyperbolic Gauss Map

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

scholarly journals New Characterizations of the Clifford Torus and the Great Sphere

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1076 ◽  
Author(s):  
Sun Mi Jung ◽  
Young Ho Kim ◽  
Jinhua Qian
Keyword(s):  
Euclidean Space ◽  
Finite Type ◽  
Three Dimensional ◽  
Gauss Map ◽  
Ruled Surfaces ◽  
Dimensional Sphere ◽  
Round Sphere ◽  
Clifford Torus ◽  
Great Sphere ◽  
Set Up

In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Gauss map. Concerning integrability and geometry, we set up new characterizations of the Clifford torus and the great sphere of 3-sphere and construct new examples of spherical ruled surfaces in a three-dimensional sphere.

scholarly journals SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP

2007 ◽  
Vol 44 (2) ◽  
pp. 407-442 ◽  
Author(s):  
Bang-Yen Chen ◽  
Huei-Shyong Lue
Keyword(s):  
Finite Type ◽  
Gauss Map

SOME CLASSIFICATIONS OF LORENTZIAN SURFACES WITH FINITE TYPE GAUSS MAP IN THE MINKOWSKI 4-SPACE

2015 ◽  
Vol 99 (3) ◽  
pp. 415-427 ◽  
Author(s):  
NURETTIN CENK TURGAY
Keyword(s):  
Minkowski Space ◽  
Finite Type ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Complete Classification ◽  
Nonzero Constant ◽  
Dimensional Minkowski Space

In this paper we study the Lorentzian surfaces with finite type Gauss map in the four-dimensional Minkowski space. First, we obtain the complete classification of minimal surfaces with pointwise 1-type Gauss map. Then, we get a classification of Lorentzian surfaces with nonzero constant mean curvature and of finite type Gauss map. We also give some explicit examples.

scholarly journals On spherical submanifolds with finite type spherical Gauss map

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Burcu Bektas ◽  
Uğur Dursun
Keyword(s):  
Finite Type ◽  
Gauss Map

AbstractChen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold M

Submanifolds with finite type Gauss map

1987 ◽  
Vol 35 (2) ◽  
pp. 161-186 ◽  
Author(s):  
Bang-yen Chen ◽  
Paolo Piccinni
Keyword(s):  
Finite Type ◽  
Minimal Surfaces ◽  
Gauss Map

In this paper we study the following problem: To what extent does the type of the Gauss map of a submanifold of Em determine the submanifold? Several results in this respect are obtained. In particular, submanifolds with 1-type Gauss map are characterized. Surfaces with 1-type Gauss map and minimal surfaces of Sm−1 with 2-type Gauss map are completely classified. Some applications are also given.

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