ﻻ يوجد ملخص باللغة العربية
Let $G$ be connected nilpotent Lie group acting locally on a real surface $M$. Let $varphi$ be the local flow on $M$ induced by a $1$-parameter subgroup. Assume $K$ is a compact set of fixed points of $varphi$ and $U$ is a neighborhood of $K$ containing no other fixed points. Theorem: If the Dold fixed-point index of $varphi_t|U$ is nonzero for sufficiently small $t>0$, then ${rm Fix} (G) cap K e emptyset$.
Let $BS(1,n) =< a, b | aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ ngeq 2$. It is known that BS(1,n) is isomorphic to the group generated by the two affine maps of the real line: $f_0(x) = x + 1$ and $h_0(x) = nx $. This pap
We show that an approximate lattice in a nilpotent Lie group admits a relatively dense subset of central $(1-epsilon)$-Bragg peaks for every $epsilon > 0$. For the Heisenberg group we deduce that the union of horizontal and vertical $(1-epsilon)$-Bra
A nilpotent Cantor action is a minimal equicontinuous action $Phi colon Gamma times frak{X} to frak{X}$ on a Cantor set $frak{X}$, where $Gamma$ contains a finitely-generated nilpotent subgroup $Gamma_0 subset Gamma$ of finite index. In this note, we
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of ${rm SU}(2),,{rm U}(2),,{rm SO}(3),,{rm SO}(3) times S^1$ and ${{rm Spin}}^{mathbb{C}}(3)$. We d
We study the Ricci tensor of left-invariant pseudoriemannian metrics on Lie groups. For an appropriate class of Lie groups that contains nilpotent Lie groups, we introduce a variety with a natural $mathrm{GL}(n,mathbb{R})$ action, whose orbits parame