Results 151 to 160 of about 752 (172)

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 ...
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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
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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
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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
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Foucault pendulum and sub-Riemannian geometry

Journal of Mathematical Physics, 2010
The well known Foucault nonsymmetrical pendulum is studied as a problem of sub-Riemannian geometry on nilpotent Lie groups. It is shown that in a rotating frame a sub-Riemannian structure can be naturally introduced. For small oscillations, three dimensional horizontal trajectories are computed and displayed in detail.
Anzaldo-Meneses, A., Monroy-Pérez, F.
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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 ...
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On the Spherical Hausdorff Measure in Step 2 Corank 2 Sub-Riemannian Geometry

SIAM Journal on Control and Optimization, 2013
Ugo Boscain, Jean-Paul Gauthier
exaly  

Sub-Riemannian Geometry

1996
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Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry

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

Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry

Journal of Geometric Mechanics, 2017
Anne Marie Svane, Stefan Sommer, Sommer Stefan   +2 more
exaly