Results 11 to 20 of about 71,381 (220)
Tangent groupoid and tangent cones in sub-Riemannian geometry [PDF]
Duke mathematical journal, 2022 Let $X_1,\cdots,X_m$ be vector fields satisfying H\"ormander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\times M\times \mathbb{R}_+^\times$ using the ...
Omar Mohsen
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Homogeneous geodesics in sub-Riemannian geometry [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2022 We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum.
A. V. Podobryaev
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Steiner and tube formulae in 3D contact sub-Riemannian geometry [PDF]
Communications in Contemporary Mathematics, 2023 We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature.
Davide Barilari, Tania Bossio
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A Formula for Popp’s Volume in Sub-Riemannian Geometry [PDF]
Analysis and Geometry in Metric Spaces, 2013 Abstract For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian ...
Barilari Davide, Rizzi Luca
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Sub-Riemannian geometry of Stiefel manifolds [PDF]
SIAM Journal on Control and Optimization, 2013 In the paper we consider the Stiefel manifold $V_{n;k}$ as a principal $U(k)$- bundle over the Grassmann manifold and study the cut locus from the unit element. We gave the complete description of this cut locus on $V_{n;1}$ and presented the sufficient condition on the general case. At the end, we study the complement to the cut locus of $V_{2k;k}$.
Christian Autenried, Irina Markina
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Shortest and straightest geodesics in sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2020 There are many equivalent definitions of Riemannian geodesics. They are naturally generalised to sub-Riemannian manifold, but become non-equivalent. We give a review of different definitions of geodesics of a sub-Riemannian manifold and interrelation between them.
D. Alekseevsky
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Bakry–Émery curvature and model spaces in sub-Riemannian geometry [PDF]
Mathematische Annalen, 2020 We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a ...
Davide Barilari +3 more
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On measures in sub-Riemannian geometry [PDF]
Séminaire de théorie spectrale et géométrie, 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
R. Ghezzi, F. Jean
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A connection theoretic approach to sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2002 We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism.
Langerock, B.
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Sub-Riemannian geometry and finite time thermodynamics Part 1: The stochastic oscillator
Discrete and Continuous Dynamical Systems. Series A, 2019 The field of sub-Riemannian geometry has flourished in the past four decades through the strong interactions between problems arising in applied science (in areas such as robotics) and questions of a pure mathematical character about the nature of space.
Yunlong Huang, P. S. Krishnaprasad
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