Results 1 to 10 of about 33,663 (156)
Characteristic Laplacian in sub-Riemannian geometry [PDF]
International Mathematics Research Notices, 2013 We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms
Daniel, Jeremy, Ma, Xiaonan
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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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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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Branching Geodesics in Sub-Riemannian Geometry [PDF]
Geometric and Functional Analysis, 2020 In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment.
Mietton, T., Rizzi, L.
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C-R Immersions and Sub-Riemannian Geometry
Axioms, 2023 On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form θ, we consider natural ϵ-contractions, i.e., contractions gϵM of the Levi form Gθ, such that the norm of the Reeb vector field T of (M, θ) is ...
Elisabetta Barletta +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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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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Integral Formulas for Almost Product Manifolds and Foliations
Mathematics, 2022 Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral formulas for almost multi-product manifolds, foliations and multiply twisted products of Riemannian, metric-affine and sub-Riemannian manifolds, to ...
Vladimir Rovenski
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Sub-Riemannian Geometry of Stiefel Manifolds [PDF]
SIAM Journal on Control and Optimization, 2014 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 $V_{2k;k}$.
Autenried, Christian, Markina, Irina
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Intrinsic fractional Taylor formula
Bruno Pini Mathematical Analysis Seminar, 2022 We consider a class of non-local ultraparabolic Kolmogorov operators and a suitable fractional Holder spaces that take into account the intrinsic sub-riemannian geometry induced by the operators.
Maria Manfredini
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