Results 51 to 60 of about 70,602 (222)
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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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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Sub-Riemannian geometry of parallelizable spheres [PDF]
Revista Matemática Iberoamericana, 2011 The first aim of the present paper is to compare various sub-Riemannian structures over the three dimensional sphere S^3 originating from different constructions. Namely, we describe the sub-Riemannian geometry of S^3 arising through
Godoy Molina , Mauricio, Markina , Irina
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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 $V_{2k;k}$.
Christian Autenried, Irina Markina
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On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry [PDF]
Geometriae Dedicata, 2020 Weyl (Zur Infinitisimalgeometrie: Einordnung der projektiven und der konformen Auffasung, Nachrichten von der K. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, Göttinger Akademie der Wissenschaften, Göttingen, 1921 ...
F. Jean, S. Maslovskaya, I. Zelenko
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Journal of Function Spaces, 2021 The group of rigid motions of the Minkowski plane with a general left-invariant metric is denoted by E1,1,gλ1,λ2, where λ1≥λ2>0. It provides a natural 2-parametric deformation family of the Riemannian homogeneous manifold Sol3=E1,1,g1,1 which is the ...
Jianyun Guan, Haiming Liu
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Integral Formulas for a Foliation with a Unit Normal Vector Field
Mathematics, 2021 In this article, we prove integral formulas for a Riemannian manifold equipped with a foliation F and a unit vector field N orthogonal to F, and generalize known integral formulas (due to Brito-Langevin-Rosenberg and Andrzejewski-Walczak) for foliations ...
Vladimir Rovenski
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Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds
Entropy, 2016 We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and
Stefan Sommer
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Journal of Differential Geometry, 1986 A sub-Riemannian or singular Riemannian geometry is given by a smoothly varying positive definite quadratic form defined only on a subbundle \(S\) of the tangent bundle \(TM\) of a differentiable manifold, \(S\) being bracket-generating, that is sections of \(S\) together with their Lie brackets generate the \(C^{\infty}(M)\)-module \(V(M)\) of vector ...
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Corrections to: ``Sub-Riemannian geometry'' [PDF]
Journal of Differential Geometry, 1989 An error in the proof of Corollary 6.2 of [1] has been pointed out by Gerard Ben-Arous. The computation of M(x,λ) in the case λo = 0 on p. 243 is incorrect, because M(x,λ) = 0 when λ0 = 0 and λjg (x) = 0 for all k. (There is also a factor of \ missing in the formula as stated for λ0 φ 0, but this is not significant.) Thus when applying the Pontryagin ...
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