Results 41 to 50 of about 70,602 (222)
Geometry of sub - Riemannian manifolds equipped with a semimetric quarter - symmetric connection
Ufa Mathematical JournalOn a sub-Riemannian manifold we introduce a semimetric quarter-symmetric connection by defining intrinsic metric connection and two structural endomorphisms preserving the distribution on a sub-Riemannian manifold.
A. Bukusheva, S. Galaev
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Sub-semi-Riemannian geometry on $H$-type groups [PDF]
, 2010 We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate indefinite metric of ...
Korolko, Anna
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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
G. Stefani +4 more
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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.
D. Barilari, Tania Bossio
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Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry [PDF]
Journal de l'École polytechnique. Mathématiques, 2023 We use techniques from nonsmooth analysis and geometric measure theory to provide new examples of complete sub-Riemannian structures satisfying the Minimizing Sard conjecture. In particular, we show that complete sub-Riemannian structures associated with
L. Rifford
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Entropy and complexity of a path in sub-Riemannian geometry [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2003 Summary: We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We
Frédéric Jean
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New second-order optimality conditions in sub-Riemannian Geometry [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2021 We study the geometry of the second-order expansion of the extended end-point map for the sub-Riemannian geodesic problem. Translating the geometric reality into equations we derive new second-order necessary optimality conditions in sub-Riemannian ...
M. J'o'zwikowski
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Symplectic, Hofer and sub-Riemannian geometry
, 2002 The purpose of this note is to make some connection between the sub-Riemannian geometry on Carnot-Caratheodory groups and symplectic geometry. We shall concentrate here on the Heisenberg group, although it is transparent that almost everything can be done on a general Carnot-Caratheodory group.
Marius Buliga
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Sub-Riemannian Curvature in Contact Geometry [PDF]
The Journal of Geometric Analysis, 2016 31 pages, 2 figures; v2: the Bonnet-Myers theorem 1.7 now holds for any contact structure; v3: final version (with expanded introduction) to appear on Journal of Geometric Analysis; v4: fixed ...
Agrachev, Andrey +2 more
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Advanced Nonlinear Studies, 2022 In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa +2 more
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