相关论文: Non-Holonomic Connections Following \'Elie Cartan

Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…

In his 1910 "Five Variables" paper, Cartan solved the equivalence problem for the geometry of $(2, 3, 5)$ distributions and in doing so demonstrated an intimate link between this geometry and the exceptional simple Lie groups of type…

We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…

This is the first part of a series of papers. The whole series aims to develop the tools for the study of all almost Hermitian symmetric structures in a unified way. In particular, methods for the construction of invariant operators, their…

In this paper we discuss how to associate a suitable non-transitive version of a Cartan connection to sub-Riemannian manifolds of corank 1 (including contact and quasi-contact sub-Riemannian manifolds) with non-necessarily constant…

The aim of the paper is to demonstrate the superiority of Cartan's method over direct methods based on differential elimination for handling otherwise intractable equivalence problems. In this sens, using our implementation of Cartan's…

Cartan's equivalence method is applied to explicitly construct invariant coframes for four branches, which are used to characterize all non-linearizable third-order ODEs with a four-dimensional Lie symmetry subalgebra under point…

We study nondifferentiable metrics occuring in general relativity via the method of equivalence of Cartan adapted to the Courant algebroids. We derive new local differential invariants naturally associated with the loci of…

Since the celebrated work by Cartan, distributions with \nobreak{small} growth vector $(2,3,5)$ have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic $(2,3,5)$-distributions and…

I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in…

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and…

We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the…

This paper surveys some results by the author and collaborators on the existence of invariant Lagrangian graphs for Tonelli Hamiltonian systems. The presentation is based on an invited talk by the author at XIX Congresso Unione Matematica…

This is the lecture 3 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The…

In this paper we study contact nonholonomic mechanical sys\-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we define different nonholonomic brackets using con\-venient…

In all the practical applications of partial differential equations, what is mostly needed and what is in fact hardest to obtains are the solutions of the system or, occasionally, some specific solutions. This work is based on a most…

This is the lecture 4 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The…

In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions on a 5-dimensional manifold. We solve the analogous problems for rank 2 distributions on an n-dimensional…

This is the lecture 2 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The…

We demonstrate that integrable abelian vortex equations on constant curvature Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections. By lifting to three dimensional group manifolds we find higher dimensional analogues…