Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Zalabova, Lenka"'
Autor:
Eisner, Jan, Zalabová, Lenka
We describe the quaternionic Heisenberg group in the dimension $7$ as a matrix group. We study the local control of a compatible left-invariant control system. We describe the impact of symmetries of the corresponding sub-Riemannian structure on the
Externí odkaz:
http://arxiv.org/abs/2404.08953
Autor:
Návrat, Aleš, Zalabová, Lenka
This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+1 equipped with a left-invariant distribution of dimension n+1 such th
Externí odkaz:
http://arxiv.org/abs/2404.01831
Autor:
Gregorovič, Jan, Zalabová, Lenka
We study first BGG operators and their solutions on homogeneous conformal geometries. We focus on conformal Killing tensors, conformal Killing--Yano forms and twistor spinors in particular. We develop an invariant calculus that allows us to find solu
Externí odkaz:
http://arxiv.org/abs/2205.08323
We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step $2$ invariant with respect to the action of $SO(3)$. We understand the geodesics as the curve
Externí odkaz:
http://arxiv.org/abs/2111.11088
Autor:
Gregorovič, Jan, Zalabová, Lenka
Publikováno v:
Journal of Geometry and Physics, 2023, 192
We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many interesting prope
Externí odkaz:
http://arxiv.org/abs/2107.10668
We study symmetries of specific left--invariant sub--Riemannian structure with filtration $(4,7)$ and their impact on sub--Riemannian geodesics of corresponding control problem. We show that there are two very different types of geodesics, they eithe
Externí odkaz:
http://arxiv.org/abs/2102.07428
Autor:
Eastwood, Michael, Zalabová, Lenka
Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the special pro
Externí odkaz:
http://arxiv.org/abs/2002.02199
Autor:
Gregorovič, Jan, Zalabová, Lenka
Publikováno v:
In Journal of Geometry and Physics October 2023 192
We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. We demonstrate the computations in the CAS Maple package DifferentialGe
Externí odkaz:
http://arxiv.org/abs/1908.03352
Autor:
Hrdina, Jaroslav, Zalabova, Lenka
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples
Externí odkaz:
http://arxiv.org/abs/1802.08480