Results 141 to 150 of about 732 (169)

MCFANet: a multi-class fusion attention network for motor imagery EEG classification. [PDF]

Front Hum Neurosci
Zhao P, Liang T, Jia H, Dayan A, Dinarès-Ferran J, Solé-Casals J.   +5 more
europepmc   +1 more source

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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 ...
Aurel Bejancu
exaly   +2 more sources

Sub-Riemannian Geometry and Optimal Transport

SpringerBriefs in Mathematics, 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 ...
Ludovic Rifford
exaly   +3 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 \(T_pM\).
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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 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.
Aurel Bejancu, Viorel Barbu, Ovidiu Ca^rjǎ   +2 more
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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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