Kinematic metric functions, which allow us to make metric measurements such as “distance”, “length” and “angle”, are often needed in robotics. However, some commonly used metric functions are not well-defined because of their dependence upon choice of reference frame. This paper presents formal and practical conditions for kinematic metric functions to be well-defined. In order to properly anal...

In this paper, we consider the Lorentzian approximations of rigid motions Minkowski plane E L 2 1,1 . By using method approximations, define notions intrinsic curvature for regular curves, geodesic curves...

Abstract The universal covering group of Euclidean motion E (2) with the general left-invariant metric is denoted by $$(\widetilde{E(2)},g_L(\lambda _1,\lambda _2)),$$ ( E 2 ) ~ , <mml:msub...

We study three Möbius invariant metrics, and three affine invariant analogs, all of which are bilipschitz equivalent to the Poincaré hyperbolic metric. We exhibit numerous illustrative examples.

We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...