Results 181 to 190 of about 892 (193)

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
Ugo Boscain, Davide Barilari, Andrei A. Agrachev   +2 more
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Geometry, Analysis and Dynamics on sub-Riemannian Manifolds

2016
These lectures focus on some probabilistic aspects related to sub-Riemannian geometry. The main intention is to give an introduction to hypoelliptic and subelliptic diffusions. The notes are written from a geometric point of view trying to minimize the weight of “probabilistic baggage” necessary to follow the arguments.
Andrei A. Agrachev, Davide Barilari, Ugo Boscain, Ugo Boscain   +3 more
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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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Geometric Control Theory and Sub-Riemannian Geometry

2014
This 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 controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to
STEFANI, GIANNA, Ugo Boscain, Mario Sigalotti, SARYCHEV, ANDREY, Jean Paul Gauthier   +4 more
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Numerical methods for sub-Riemannian geometry [PDF]

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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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.
A. Anzaldo-Meneses, F. Monroy-Pérez
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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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A parallelism for contact conformal sub-Riemannian geometry

Forum Mathematicum, 1998
The authors introduce the notion of sub-conformal structure on a contact manifold and give a complete set of local invariants for such structures, which provides a generalisation of the well-known CR-structure on hypersurfaces of almost complex manifolds.
José Miguel Martins. Veloso, Elisha Falbel   +1 more
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Sub-Riemannian Geometry and Optimal Transport

2014
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the ...
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Sub-Riemannian geometry and nonholonomic mechanics

AIP Conference Proceedings, 2011
The purpose of the present paper is to study the geometry of a sub‐Riemannian manifold and to apply the results to the nonholonomic mechanical systems. First, we construct a linear connection on the horizontal distribution and obtain some Bianchi identities for it.
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