Related papers: Induced structures on product of spheres
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
In this paper we define and construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.
We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
We develop the basic formulae of hyperspherical trigonometry in multidimensional Euclidean space, using multidimensional vector products, and their conversion to identities for elliptic functions. We show that the basic addition formulae…
There are several well-known characterizations of the sphere as a regular surface in the Euclidean space. By means of a purely synthetic technique, we get a rigidity result for the sphere without any curvature conditions, nor completeness…
The main results of the paper are Proposition 3 and 4 which provide an effective way to construct minimal hypersurfaces in a Euclidean space. We demonstrate our technique by several new examples. This note is English translation of an…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…
We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter…
The purpose of this paper is to investigate the large inductive dimension of the remainder of the Smirnov compactification of the n-dimensional Euclidean space with the usual metric, and give an application of it.
We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to…
Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we investigate the metric structure induced on $S$ by $M$, in the sense of length spaces. First, we define a coefficient $\widehat K$ at characteristic points that determines…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
We consider the gauge potential A and argue that the minimum value of the volume integral of A squared (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice…
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
Recent researches on designs for computer experiments with both qualitative and quantitative factors have advocated the use of marginally coupled designs. This paper proposes a general method of constructing such designs for which the…
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres…