Results 31 to 40 of about 33,123 (219)
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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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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A Comprehensive Introduction to Sub-Riemannian Geometry [PDF]
, 2019 Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several ...
Agrachev, Andrei +2 more
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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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Sub-Lorentzian Geometry on Anti-De Sitter Space [PDF]
, 2008 Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group.
Beals +19 more
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Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot
Pacific Journal of Mathematics for Industry, 2018 The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the
Bernard Bonnard +3 more
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On 4-dimensional Einsteinian manifolds with parallel null distribution [PDF]
ریاضی و جامعه, 2023 In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this purpose, we first obtain the equations, which are known as Einstein's equations, that lead to finding the mentioned manifolds and then, we reduce Einstein's
Mehdi Jafari
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Gauss-Bonnet theorem in Lorentzian Sasakian space forms
AIMS Mathematics, 2021 In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of 3-dimensional Lorentzian Sasakian space forms.
Haiming Liu, Jiajing Miao
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Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part I [PDF]
, 2015 We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub-Riemannian manifolds obtained from Riemannian foliations ...
Grong, Erlend, Thalmaier, Anton
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