Results 31 to 40 of about 894 (54)

Metric lines in the jet space

Analysis and Geometry in Metric Spaces
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
doaj   +1 more source

Superrigid subgroups of solvable Lie groups

, 1996
Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_G\Gamma$ has the same Zariski closure as $\Ad G$. If $\alpha \colon \Gamma \to \GL_n(\real)$ is any finite-dimensional representation of~$\Gamma $,we show ...
Communicated Roe Goodman, Dave Witte
core   +4 more sources

Leibniz's rule on two-step nilpotent Lie groups

, 2016
Let $\mathfrak{g}$ be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows to define a generalized multiplication $f \# g = (f^{\vee} * g^{\vee})^{\wedge}$ of two functions in ...
Bekała, Krystian
core   +1 more source

Symmetry Algebras of the Canonical Lie Group Geodesic Equations in Dimension Three [PDF]

, 2018
For each of the two and three-dimensional indecomposable Lie algebras the geodesic equations of the associated canonical Lie group connection are given.
Ghanam, Ryad, Thompson, Gerard
core   +1 more source

On line bundles arising from the LCK structure over locally conformal Kähler solvmanifolds

Complex Manifolds
We can construct a real line bundle arising from the locally conformal Kähler (LCK) structure over an LCK manifold. We study the properties of this line bundle over an LCK solvmanifold whose complex structure is left-invariant. Mainly, we prove that this
Yamada Takumi
doaj   +1 more source

Lie Symmetries of the Canonical Geodesic Equations for Four-Dimensional Lie Groups [PDF]

, 2018
For each of the four-dimensional indecomposable Lie algebras the geodesic equations of the associated canonical Lie group connection are given. In each case a basis for the associated Lie algebra of symmetries is constructed and the corresponding Lie ...
Ghanam, Ryad, Thompson, Gerard
core   +2 more sources

The triangle inequality for graded real vector spaces of length 5

, 2019
In this paper, we prove that a natural candidate for a homogeneous norm on a graded Lie algebra of length 5 satisfies the triangle inequality which answers Moskowitz's ...
Sriwongsa, Songpon, Wiboonton, Keng
core  

Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]

J Geom Anal, 2023
Lerario A, Tripaldi F.
europepmc   +1 more source

On rectifiable measures in Carnot groups: representation. [PDF]

Calc Var Partial Differ Equ, 2022
Antonelli G, Merlo A.
europepmc   +1 more source

Polynomial and horizontally polynomial functions on Lie groups. [PDF]

Ann Mat Pura Appl, 2022
Antonelli G, Le Donne E.
europepmc   +1 more source