scholarly journals CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP

2013 ◽  
Vol 50 (4) ◽  
pp. 1345-1356 ◽  
Author(s):  
Young Ho Kim ◽  
Nurettin Cenk Turgay
Keyword(s):  
Gauss Map ◽  
Helicoidal Surfaces

scholarly journals HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE

2010 ◽  
Vol 47 (4) ◽  
pp. 859-881 ◽  
Author(s):  
Mie-Kyung Choi ◽  
Young-Ho Kim ◽  
Huili Liu ◽  
Dae-Won Yoon
Keyword(s):  
Gauss Map ◽  
Helicoidal Surfaces

scholarly journals HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

2009 ◽  
Vol 46 (1) ◽  
pp. 215-223 ◽  
Author(s):  
Mie-Kyung Choi ◽  
Dong-Soo Kim ◽  
Young-Ho Kim
Keyword(s):  
Gauss Map ◽  
Helicoidal Surfaces

scholarly journals HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE II

2009 ◽  
Vol 46 (3) ◽  
pp. 567-576 ◽  
Author(s):  
Mie-Kyung Choi ◽  
Young-Ho Kim ◽  
Gi-Chan Park
Keyword(s):  
Gauss Map ◽  
Helicoidal Surfaces

scholarly journals Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

2021 ◽  
Vol 9 ◽  
Author(s):  
Joseph Malkoun ◽  
Peter J. Olver
Keyword(s):  
Convex Hull ◽  
Convex Geometry ◽  
Gauss Map ◽  
Parameter Family ◽  
Convex Hulls ◽  
Dimensional Sphere ◽  
Continuous Maps ◽  
Dimensional Boundary

Abstract Given n distinct points $\mathbf {x}_1, \ldots , \mathbf {x}_n$ in $\mathbb {R}^d$ , let K denote their convex hull, which we assume to be d-dimensional, and $B = \partial K $ its $(d-1)$ -dimensional boundary. We construct an explicit, easily computable one-parameter family of continuous maps $\mathbf {f}_{\varepsilon } \colon \mathbb {S}^{d-1} \to K$ which, for $\varepsilon> 0$ , are defined on the $(d-1)$ -dimensional sphere, and whose images $\mathbf {f}_{\varepsilon }({\mathbb {S}^{d-1}})$ are codimension $1$ submanifolds contained in the interior of K. Moreover, as the parameter $\varepsilon $ goes to $0^+$ , the images $\mathbf {f}_{\varepsilon } ({\mathbb {S}^{d-1}})$ converge, as sets, to the boundary B of the convex hull. We prove this theorem using techniques from convex geometry of (spherical) polytopes and set-valued homology. We further establish an interesting relationship with the Gauss map of the polytope B, appropriately defined. Several computer plots illustrating these results are included.

scholarly journals A note on surfaces with prescribed oriented Euclidean Gauss map

2005 ◽  
Vol 2005 (4) ◽  
pp. 537-543
Author(s):  
Ricardo Sa Earp ◽  
Eric Toubiana
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Gauss Map ◽  
Compatibility Relation ◽  
Hyperbolic Gauss Map ◽  
Conformal Immersion

We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. Our approach depends on geometric quantities, that is, the hyperbolic Gauss mapGand formulae obtained in hyperbolic space. We use the idea that the Euclidean Gauss map and the hyperbolic Gauss map with some compatibility relation determine a conformal immersion, proved in a previous paper.

On the geometry of the Gauss map of conformal foliations by lines

2004 ◽  
Vol 136 (1) ◽  
pp. 247-255
Author(s):  
JEAN-MARIE BUREL ◽  
SIGMUNDUR GUDMUNDSSON
Keyword(s):  
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
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