ON THE THEORY OF TWO-DIMENSIONAL SURFACES IN EUCLIDEAN SPACE

2003 ◽  
Author(s):  
G. GANCHEV ◽  
V. MILOUSHEVA
Keyword(s):  
Euclidean Space ◽  
Two Dimensional ◽  
Surfaces In Euclidean Space

scholarly journals Developable surfaces in Euclidean space

1999 ◽  
Vol 66 (3) ◽  
pp. 388-402 ◽  
Author(s):  
Vitaly Ushakov
Keyword(s):  
Euclidean Space ◽  
Arbitrary Dimension ◽  
Main Tool ◽  
Moving Frame ◽  
Two Dimensional ◽  
Surfaces In Euclidean Space ◽  
Moving Frame Method ◽  
Frame Method ◽  
Euclidean Three Space ◽  
Three Space

AbstractThe classical notion of a two-dimensional develpable surface in Euclidean three-space is extended to the case of arbitrary dimension and codimension. A collection of characteristic properties is presented. The theorems are stated with the minimal possible integer smoothness. The main tool of the investigation is Cartan's moving frame method.

An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Taiga Kumagai
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Asymptotic Analysis ◽  
Open Subset ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Two Dimensional ◽  
Jacobi Equations ◽  
Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

ON EUCLIDEAN G-MANIFOLDS WHICH HAVE TWO DIMENSIONAL ORBIT SPACES

2011 ◽  
Vol 22 (03) ◽  
pp. 399-406
Author(s):  
R. MIRZAIE
Keyword(s):  
Euclidean Space ◽  
Half Plane ◽  
Lie Group ◽  
Orbit Space ◽  
Two Dimensional ◽  
Orbit Spaces ◽  
Group Of Isometries ◽  
Connected Lie Group

We show that the orbit space of Euclidean space, under the action of a closed and connected Lie group of isometries is homeomorphic to a plane or closed half-plane, if the action is of cohomogeneity two.

Skew mean curvature flow

2019 ◽  
Vol 21 (01) ◽  
pp. 1750090
Author(s):  
Chong Song ◽  
Jun Sun
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Embedding Theorem ◽  
Sobolev Type ◽  
Two Dimensional ◽  
Initial Value ◽  
Codimension Two ◽  
Surfaces In Euclidean Space ◽  
Short Time

The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of a short-time solution to the initial value problem of the SMCF of compact surfaces in Euclidean space [Formula: see text]. A Sobolev-type embedding theorem for the second fundamental forms of two-dimensional surfaces is also proved, which might be of independent interest.

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