Related papers: Magnetic trajectories on 2-step nilmanifolds
As a generalization and extension of JMP 54 (2013) 022901, the classical dynamics of three non-relativistic Coulomb charges $(e_1, m_1)$, $(e_2, m_2)$ and $(e_3, m_3)$ on the plane placed in a constant magnetic field perpendicular to the…
We study left invariant contact forms and left invariant symplectic forms on Lie groups. We give the classification of all symplectic structures on nilpotent Lie algebras up the dimension 6.
The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections of submersions of Riemannian manifolds, and applied to sections of Riemannian vector bundles and their sphere…
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the…
The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that any 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step…
Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…
This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous…
For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl-Pedersen calculus of their…
In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated…
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and…
The eta invariant appears regularly in index theorems but is known to be directly computable from the spectrum only in certain examples of locally symmetric spaces of compact type. In this work, we derive some general formulas useful for…
Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…
In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups constructed in \cite{kennedy88b} using a symplectic structure can be recovered from canonical geometric mechanics with a bi-invariant metric. Hence we…
The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are found. The manifold admits a four-parameter…
Inspired by orbit parametrizations in arithmetic statistics, we explain how to construct families of curves associated to certain nilpotent elements in $\mathbb{Z}/m\mathbb{Z}$-graded Lie algebras, generalizing work of Thorne to the $m\geq…
The classical two-dimensional problem of non-interacting electrons scattered by short-range impurity centers in the presence of magnetic field is investigated both analytically and numerically. A strong magnetoresistance exists in such a…
We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.
In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of…
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature.…
We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat…