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Cones and Cartan geometry
(Elsevier Science, 2021-10)
We show that the extended principal bundle of a Cartan geometry of type (A(m,R),GL(m,R)), endowed with its extended connection ωˆ, is isomorphic to the principal A(m,R)-bundle of affine frames endowed with the affine ...
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences
(Springer Berlin Heidelberg, 2013)
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In ...
Luis Santaló and classical field theory
(Springer Verlag Berlín, 2019-11)
Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic ...
A Basis Theorem for 2-rigs and Rig Geometry
(Centre National de la Recherche Scientifique. Faculté des Sciences. Laboratoire amiénois de mathématique fondamentale et appliquée, 2021-10)
Un semi-anneau unitaire commutatif (ou rig, en abrégé) est integral si 1 + x = 1. Nous montrons que, de meme que le classique ‘gros topos’ de Zariski associé a un corps algébriquement clos, le topos classifiant Z des rigs ...
Folds and Refolds: Space Generation, Shapes, and Complex Components
(IGI Global, 2016)
Geometry and architecture both have a long trajectory in the history of western thought. Geometry offersthe possibility to interpret the physical structure of the world and to develop rational thinking, whilearchitecture ...
Vacua of exotic massive 3D gravity
(Springer, 2018-08)
We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary ...
A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
(Springer Berlin Heidelberg, 2013)
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In ...
A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences
(SPRINGER, 2013-01-01)
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In ...
Quantum toric degeneration of quantum flag and Schubert varieties
(Springer, 2020-09)
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative ...