In 3-dimensional Euclidean space Scherk second surfaces are singly periodic embedded minimal surfaces with 4 planar ends. In this paper, we obtain a natural generalization of Scherk’s second surfaces in higher dimensional Euclidean spaces. In particular we show that, in higher dimensional Euclidean spaces R, for n ≥ 3, there exists n−1-periodic embedded minimal hypersurfaces with 4 hyperplanar ...

This paper presents an overview of various matrix manifolds that are commonly used in computer vision applications. It covers the following manifoldsLie groups, Stiefel manifolds, Grassmann manifolds and Riemannian manifolds. A manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has ...

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n−d) curvilinear coordinates parametrizing the manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n−d) configuration coordinates. Starting from this...

The one-dimensional N ×N -matrix Chern-Simons action is given, for large N and for slowly varying fields, by the (2k + 1)-dimensional Chern-Simons action SCS , where the gauge fields in SCS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by t...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

We show that the three-dimensional layers-of-maxima problem can be solved in o(n log n) time in the word RAM model. Our algorithm runs in O(n(log log n)) deterministic time or O(n(log log n)) expected time and uses O(n) space. We also describe a deterministic algorithm that uses optimal O(n) space and solves the three-dimensional layers-of-maxima problem in O(n log n) time in the pointer machine

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...