Results 21 to 30 of about 798 (51)

Observability on the classes of non-nilpotent solvable three-dimensional Lie groups

Open Mathematics
In control theory, researchers need to understand a system’s local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space defined by an ...
Ayala Victor, Cavalheiro Thiago Matheus, Santana Alexandre J.   +2 more
doaj   +1 more source

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

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

Gradings on Lie algebras with applications to infra-nilmanifolds

, 2016
In this paper, we study positive as well as non-negative and non-trivial gradings on finite dimensional Lie algebras. We give a different proof that the existence of such a grading on a Lie algebra is invariant under taking field extensions, a result ...
Deré, Jonas
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

Invariant and non-invariant almost complex structures on compact quotients of Lie groups

Complex Manifolds
In this article, we briefly survey the classical problem of understanding which Lie algebras admit a complex structure, put in the broader perspective of almost complex structures with special properties.
Sillari Lorenzo, Tomassini Adriano
doaj   +1 more source

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