We prove that any analytic set in $\C^n$ with a unique tangent cone at infinity is an algebraic set. the degree of complex $\C^n$, which Lipschitz normally embedded infinity, equal to its infinity.

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense any linear of horizontal tangent realized by a global isometry. will show these have canonical partial connection defined on their bundle. However, unlike Riemannian case, such are not uniquely determined curvature and metric cone. Furthermore, number invariants needed to determine model with same cone ge...

We develop a mathematical framework for describing local features of a geometric object— such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a tangent complex for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic fe...

When rendering objects with hardware tessellation, back-facing patches should be culled as early as possible to avoid unnecessary surface evaluations, and setup costs for the tessellator and rasterizer. For dynamic objects the popular cone-of-normals approach is usually approximated using tangent and bitangent cones. This is faster to compute, but less effective. We present a novel approach usi...

The aim of the article is to study Betti numbers tangent cone Gorenstein monomial curves in affine 4-space. If $C_S$ a noncomplete intersection curve whose Cohen--Macaulay, we show that possible sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).

We exhibit an example of a homogeneous Lorentzian manifold G/H whose homogeneous geodesics form just the light-cone and a hyperplane in the tangent space. For all light-like homogeneous geodesics, the natural parameter of the orbit is not the affine parameter of the geodesic.

Tangent cones Let A ⊆ R be a closed semialgebraic (s.a.) set and assume from now on that the origin O is not an isolated point of A. We recall that the tangent cone to A at O is the set C(A) = {u ∈ R|u = lim k→∞ tkxk}, where {xk} ⊂ A tends to O and {tk} ⊂ R. If we allow tk ∈ R only, we get what we call the tangent semicone to A at O, which we denote with C(A). It is easy to show that both C(A) ...

Under the relaxed constant rank condition, introduced by Minchenko and Stakhovski, we prove that linearized cone is contained in tangent (Abadie condition) for sets represented as solution to systems of finite numbers inequalities equations given continuously differentiable functions defined on Banach spaces.