Results 1 to 10 of about 228,181 (46)

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.
Chang, Der-Chen, Markina, Irina, Vasil'ev, Alexander   +2 more
core   +2 more sources

Sard property in Carnot groups [PDF]

, 2021
In this work we introduce the topic of sub-Riemannian geometry from an elementary viewpoint. Sub-Riemannian geometry is a quite modern field of differential geometry.
Nalon, Luca
core   +1 more source

Lectures on Finslerian Geometry [PDF]

arXiv, 2023
Lecture notes on Finsler ...
arxiv  

Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry [PDF]

, 2017
On a sub-Riemannian manifold we define two type of Laplacians. The \emph{macroscopic Laplacian} $\Delta_\omega$, as the divergence of the horizontal gradient, once a volume $\omega$ is fixed, and the \emph{microscopic Laplacian}, as the operator ...
Boscain, Ugo, Neel, Robert, Rizzi, Luca
core   +3 more sources

On the Hausdorff volume in sub-Riemannian geometry [PDF]

, 2011
For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous
A. Agrachev, A. Agrachev, A. Bonfiglioli, A.A. Agrachev, A.A. Agrachev, A.A. Agrachev, A.A. Agrachev, Andrei Agrachev, B. Franchi, Davide Barilari, F. Jean, H. Federer, I. Chavel, J. Mitchell, J.-P. Gauthier, J.-P. Gauthier, J.-P. Gauthier, L. Ambrosio, L. Ambrosio, L. Capogna, L.P. Rothschild, P. Rashevsky, R. Montgomery, R. Monti, R.M. Bianchini, T. Kato, Ugo Boscain, V. Jurdjevic, W.-L. Chow, Z.M. Balogh, Z.M. Balogh   +30 more
core   +2 more sources

The Generalised Complex Geometry of $(p,q)$ Hermitian Geometries [PDF]

, 2018
We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised K\"{a}hler geometry for $(2,2)$, generalised hyperk\"{a}hler geometry for $(4,2)$, strong K\"{a}hler with torsion geometry for $(2,1)$ and strong hyperk\"{a}hler with torsion geometry for $(4,1)$.
arxiv   +1 more source

Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D [PDF]

, 2017
We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$.
Bekkers, Erik J., Chen, Da, Portegies, Jorg M.   +2 more
core   +2 more sources

Topics in sub-Riemannian geometry [PDF]

, 2016
This thesis is concerned with three different problems in sub-Riemannian geometry faced during my PhD. The first one is a problem in differential geometry and is about the local conformal classification of a certain class of sub-Riemannian structures. In
Boarotto, Francesco
core   +1 more source

The rolling problem: overview and challenges

, 2012
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the ...
A Agrachev, A Agrachev, A Agrachev, A Chelouah, A Marigo, A Marigo, AM Bloch, AV Borisov, Cartan, Cartan, DJ Montana, DW Stroock, E Grong, EP Hsu, F Alouges, G Bor, H Sussmann, I Zelenko, I Zelenko, IM Singer, J Zimmerman, J-M Bismut, K Hüper, K Hüper, K Nomizu, M Godoy Molina, M Godoy Molina, P Rouchon, PB Gilkey, PE Jupp, R Bryant, R Montgomery, R Murray, RW Sharpe, S Kobayashi, SA Chaplygin, SA Chaplygin, T Sakai, V Jurdjevic, V Jurdjevic, V Jurdjevic, Y Chitour, Y Chitour, Y Chitour, Z Li   +44 more
core   +2 more sources

Braided spaces with dilations and sub-riemannian symmetric spaces [PDF]

, 2011
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces.
Buliga, Marius
core