Results 31 to 40 of about 1,124 (81)
Moving frames for cotangent bundles
, 2002 Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep.
Ehlers, K. M. +2 more
core +1 more source
Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups [PDF]
, 2014 Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liouville integrability and superintegrability are ...
Mashtakov, Alexey P., Sachkov, Yuri L.
core +1 more source
A counterexample to gluing theorems for MCP metric measure spaces
, 2018 Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq \kappa$ is an Alexandrov space with the same dimension and satisfying the same curvature lower ...
Rizzi, Luca
core +2 more sources
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces, 2015 Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj +1 more source
, 2013 We study the classification of area-stationary and stable $C^2$ regular surfaces in the space of the rigid motions of the Minkowski plane E(1,1), equipped with its sub-Riemannian structure.
Galli, Matteo
core +1 more source
Rigidity of quasiconformal maps on Carnot groups [PDF]
, 2013 We show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between negatively curved solvable Lie groups.
arxiv +1 more source
Polarizing Anisotropic Heisenberg Groups [PDF]
Analysis and Mathematical Physics 2020, 2019 We expand the class of polarizable Carnot groups by implementing a technique to polarize anisotropic Heisenberg groups.
arxiv +1 more source
Analysis and Geometry in Metric SpacesIn the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
doaj +1 more source
Riemannian and Sub-Riemannian geodesic flows
, 2015 In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of
Grong, Erlend, Molina, Mauricio Godoy
core +1 more source
Isoperimetric problem in H-type groups and Grushin spaces [PDF]
, 2014 We study the isoperimetric problem in H-type groups and Grushin spaces, emphasizing a relation between them. We prove existence, symmetry and regularity properties of isoperimetric sets, under a symmetry assumption that depends on the dimension.
arxiv +1 more source