Results 151 to 160 of about 3,198,197 (181)

Curvature in sub-Riemannian geometry

Journal of Mathematical Physics, 2012
We study curvature problems on a nearly Riemannian manifold, which is a sub-Riemannian manifold (M, HM, g, VM) whose adapted tensor field given by (2.2) vanishes identically. First, we prove the existence and uniqueness of what we call horizontal Riemannian connection, which is a torsion-free and metric linear connection ∇ on the horizontal ...
exaly   +2 more sources

Geometric Control Theory and Sub-Riemannian Geometry

Springer INdAM Series, 2014
International audienceThis volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying ...
Sigalotti, Mario, Gauthier, Jean-Paul, Stefani, Gianna, Boscain, Ugo, Sarychev, Andrey   +4 more
exaly   +6 more sources

Sub-Riemannian Geometry

2009
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context.
Ovidiu Calin, Der-Chen Chang
openaire   +1 more source

The tangent space in sub-Riemannian geometry

Journal of Mathematical Sciences, 1996
Let \(M\) be a sub-Riemannian manifold. Suppose that the Hörmander condition holds. Then to each point \(p\in M\) we can associate its degree of nonholonomy \(r(p)\) which counts how many bracket iterations of horizontal vector fields near \(p\) are needed to span the tangent space \(T_pM\).
openaire   +2 more sources

Characterizations of hamiltonian geodesics in sub-riemannian geometry

Journal of Dynamical and Control Systems, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alcheikh, M., Orro, P., Pelletier, F.
openaire   +1 more source

Paths in sub-Riemannian geometry

2007
In sub-Riemannian geometry only horizontal paths — i.e. tangent to the distribution — can have finite length. The aim of this talk is to study non-horizontal paths, in particular to measure them and give their metric dimension. For that we introduce two metric invariants, the entropy and the complexity, and corresponding measures of the paths depending
openaire   +1 more source

Volumes in Sub-Riemannian Geometry

2019
In this chapter we investigate the notion of the intrinsic volume in sub-Riemannian geometry in the case of "equiregular" structures. In particular we consider the Popp and the Hausdorff volumes. On
openaire   +1 more source

Introduction to geodesics in sub-Riemannian geometry

2016
Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds.
Agrachev, Andrei, Barilari, Davide, Boscain, Ugo   +2 more
openaire   +3 more sources

Numerical methods for sub-Riemannian geometry

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003
Consider a sub-Riemannian geometry (U,/spl Delta/,g) where U is a neighborhood of 0 in R/sup n/, /spl Delta//spl sub/TR/sup n/ a distribution of constant rank m and g a Riemannian metric defined on /spl Delta/. One of the main questions related to a given sub-Riemannian structure is the description of the conjugate and cut loci, of the sphere and the ...
openaire   +1 more source

Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry

Advances in Mathematics, 2017
Ugo Boscain, Luca Rizzi, Robert W. Neel
exaly