A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Robust and Nonlinear Control"
DOI: 10.1002/rnc.5085
Abstract: We present a geometric discrete‐time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the control trajectories in addition to pointwise constraints on the states and control actions directly at the… read more here.
Keywords: lie; pontryagin maximum; maximum principle; matrix lie ... See more keywords
Negative Ricci curvature on some non-solvable Lie groups II
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-019-02310-z
Abstract: We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products $${\mathfrak {l}}= ({\mathfrak {a}} \oplus {\mathfrak {u}} ) < imes {\mathfrak {n}}$$… read more here.
Keywords: mathfrak; ricci curvature; lie groups; mathfrak mathfrak ... See more keywords
On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups
Sign Up to like & getrecommendations! Published in 2021 at "Geometriae Dedicata"
DOI: 10.1007/s10711-020-00532-8
Abstract: This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review… read more here.
Keywords: lipschitz classification; lie groups; classification; quasi isometric ... See more keywords
The General Solution for Affine Control Systems on Lie Groups
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-022-09591-4
Abstract: The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we… read more here.
Keywords: affine control; systems lie; solution; lie groups ... See more keywords
Emergent Dynamics of a Generalized Lohe Model on Some Class of Lie Groups
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DOI: 10.1007/s10955-017-1797-8
Abstract: We introduce a Lohe group which is a new class of matrix Lie groups and present a continuous dynamical system for the synchronization of group elements in a Lohe group. The Lohe group includes classical… read more here.
Keywords: phase locked; lie groups; lohe model; group ... See more keywords
Non-embedding theorems of nilpotent Lie groups and sub-Riemannian manifolds
Sign Up to like & getrecommendations! Published in 2018 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-020-0823-3
Abstract: We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD (0, N ) with… read more here.
Keywords: nilpotent lie; non embedding; lie groups; embedding theorems ... See more keywords
Green-type identities for Rockland operators on graded Lie groups
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DOI: 10.1007/s11785-018-0824-3
Abstract: This paper considers the analogues of Green-type formulae for Rockland operators on graded Lie groups. Furthermore, we also discuss some of their consequences. read more here.
Keywords: rockland operators; lie groups; green type; graded lie ... See more keywords
Nonexistence Results for the Hyperbolic-Type Equations on Graded Lie Groups
Sign Up to like & getrecommendations! Published in 2020 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-020-00919-6
Abstract: In this paper, we deal with systems of wave and pseudo-hyperbolic equations. Some semilinear equations for hypoelliptic operators on $${\mathbb {R}}^{n}$$, Heisenberg groups, stratified Lie groups and graded Lie groups are studied. In particular, we… read more here.
Keywords: pseudo hyperbolic; hyperbolic equations; lie groups; nonexistence results ... See more keywords
Yamabe Flow On Nilpotent Lie Groups
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DOI: 10.1007/s41980-019-00317-0
Abstract: In this paper, we consider the Yamabe flow on Lie groups with left invariant metrics in particular case on the higher dimensional classical Heisenberg nilpotent Lie groups and the higher dimensional quaternion Lie groups. We… read more here.
Keywords: groups yamabe; lie; nilpotent lie; lie groups ... See more keywords
Geodesic orbit metrics on compact simple Lie groups arising from flag manifolds
Sign Up to like & getrecommendations! Published in 2018 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2018.06.004
Abstract: Abstract In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of flag manifolds. We prove that all these left-invariant geodesic orbit metrics… read more here.
Keywords: geodesic orbit; simple lie; flag manifolds; lie groups ... See more keywords
On the smoothness of some quotients of Banach-Lie groups
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DOI: 10.1016/j.difgeo.2019.101556
Abstract: Abstract Quotients of Banach-Lie groups are regarded as topological groups with Lie algebra in the sense of Hofmann-Morris on the one hand, and as Q-groups in the sense of Barre-Plaisant on the other hand. For… read more here.
Keywords: lie groups; lie algebra; smoothness quotients; banach lie ... See more keywords