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The Toric Geometry of Triangulated Polygons in Euclidean Space
Toric Geometry Triangulated Polygons Euclidean Space
2015/10/14
Speyer and Sturmfels associated Grobner toric degenerations Gr¨2(Cn)T of Gr2(Cn) witheach trivalent tree T having n leaves. These degenerations induce toric degenerations Mr T of Mr, the space of n or...
The Symplectic Geometry of Polygons in Euclidean Space
Symplectic Geometry Polygons Euclidean Space
2015/10/14
The Symplectic Geometry of Polygons in Euclidean Space.
Recently, the Isomap procedure [1] was proposed as a new way to recover a low-dimensional
parametrization of data lying on a low-dimensional submanifold in high-dimensional space.
The method assumes...
On continuous expansions of configurations of points in Euclidean space
regular simplex expanding configuration continuous expansion
2011/8/22
Abstract: For any two configurations of ordered points $p=(p_{1},...,\p_{N})$ and $q=(q_{1},...,q_{N})$ in Euclidean space $E^d$ such that $q$ is an expansion of $p$, there exists a continuous expansi...
Uniform approximation of a class of multivariable trigonometric interpolation polynomials in Euclidean space
triangle summation operator uniform convergence
2010/9/25
To improve the uniform convergence of the classical Lagrange operators of several variables, we construct a new operator with a class of summation factors. It is proved that the new operator converges...
Complete systems of differential invariants of vector fields in a euclidean space
Vector field Christoffel symbol Bonnet theorem Differential invariant
2010/12/21
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(...
A_2-singularities of hypersurfaces with non-negative sectional curvature in Euclidean space
hypersurfaces non-negative sectional curvature Euclidean space
2010/11/11
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. A...
Bi-Lipschitz Embeddability of the Grushin Plane into Euclidean Space
Bi-Lipschitz Embeddability the Grushin Plane Euclidean Space
2010/11/9
Many sub-Riemannian manifolds like the Heisenberg group do not admit bi- Lipschitz embedding into any Euclidean space. In contrast, the Grushin plane admits a bi-Lipschitz embedding into some Euclidea...
Some Characterizations of Rectifying Curves in the Euclidean Space E4
Rectifying curve Frenet equations curvature
2010/2/25
In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement N\perp of its principal normal vector field N. In particular,...
Some Graph Type Hypersurfaces in a Semi-Euclidean Space
graph lightlike hypersurface minimal semi-Euclidean space totally geodesic
2010/3/1
We consider some graph type hypersurfaces in a semi-Euclidean space \Bbb Rn+1q and give conditions of the dimension n+1 and the index q when a hypersurface is lightlike, totally geodesic and minimal.
Structure of m-Dimensional Implicitly Defined Surfaces in n-Dimensional Euclidean Space En
m-Dimensional Implicitly n-Dimensional Euclidean Space En
2010/3/3
We consider the structure of the surface in the given point, if we vary all its normals in this point.
The Hessian Tensor on a Hypersurface in Euclidean Space and Otsuki's Lemma
Hypersurface Euclidean Space Otsuki's Lemma
2010/3/5
The purpose of this paper is to obtain a condition for a hypersurface in Euclidean space with belongs to Hessian Tensor and is to give an alternative proof of Otsuki's lemma by applying this condition...