Results 41 to 50 of about 1,380,597 (301)
Nonassociative Riemannian geometry by twisting [PDF]
Journal of Physics: Conference Series, 2010 Many quantum groups and quantum spaces of interest can be obtained by cochain (but not cocycle) twist from their corresponding classical object. This failure of the cocycle condition implies a hidden nonassociativity in the noncommutative geometry already known to be visible at the level of differential forms.
Shahn Majid, Edwin J. Beggs
openaire +5 more sources
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 +2 more
core +2 more sources
On Riemannian and non-Riemannian Optimisation, and Optimisation Geometry [PDF]
IFAC-PapersOnLine, 2021 Abstract Abstract Optimisation algorithms such as the Newton method were first generalised to manifolds by generalising the components of the algorithm directly: gradients were replaced by Riemannian gradients, straight lines were replaced by geodesics, and so forth. This meant having to endow the manifold with a Riemannian metric. Traditionally then,
Lefevre, J +4 more
openaire +3 more sources
On some conformally einstein manifolds of dimension four [PDF]
ریاضی و جامعه, 2022 We study an important family of four-dimensional pseudo-Riemannian manifolds, i.e. generalized symmetric spaces, in terms of conformal geometry. Generalized symmetric spaces were introduced by geometers as an extension of symmetric spaces, and a detailed
Amirhesam Zaeim +2 more
doaj +1 more source
Riemannian Curl in Contact Geometry [PDF]
International Mathematics Research Notices, 2014 16 pages, Theorem 5.2.1 ...
Bouarroudj, S., Ovsienko, Valentin
openaire +3 more sources
Teleparallel Gravity: Foundations and Observational Constraints—Editorial
Universe, 2021 Einstein’s formulation of general relativity as a theory based on the geometry of curvature was a necessity due to Riemannian geometry being the only fully developed framework at the time [...]
Sebastian Bahamonde, Jackson Levi Said
doaj +1 more source
The Riemannian Geometry of Deep Generative Models [PDF]
2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), 2017 Deep generative models learn a mapping from a low-dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space.
Hang Shao, Abhishek Kumar, P. Fletcher
semanticscholar +1 more source
Riemannian foliations of bounded geometry [PDF]
Mathematische Nachrichten, 2014 Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart‐free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation charts. For this type of charts, it is also shown that the derivatives of the changes of coordinates are uniformly ...
Jesús A. Álvarez López +2 more
openaire +3 more sources
A Comprehensive Introduction to Sub-Riemannian Geometry
, 2019 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or ...
A. Agrachev, D. Barilari, U. Boscain
semanticscholar +1 more source
Quantum Riemannian geometry and particle creation on the integer line [PDF]
Classical and quantum gravity, 2018 We construct noncommutative or ‘quantum’ Riemannian geometry on the integers as a lattice line with its natural 2-dimensional differential structure and metric given by arbitrary non-zero edge square-lengths .
S. Majid
semanticscholar +1 more source