Results 141 to 150 of about 33,682 (168)

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
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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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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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On measures in sub-Riemannian geometry

2017
In \cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions.
Ghezzi, Roberta, Jean, Fr��d��ric   +1 more
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The tangent space in sub-Riemannian geometry

Journal of Mathematical Sciences, 1994
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 \(T_pM\).
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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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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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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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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.
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Sub-Riemannian Geometry and Hypoelliptic Operators

2017
In this course we carefully define the notion of a non-holonomic manifold, which is a manifold with a certain non-integrable smooth sub-bundle of the tangent bundle, also called a distribution. We define such concepts as horizontal distributions, bracket generating condition for distributions, a sub-Riemannian structure, hypoelliptic and subelliptic ...
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