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Iterated Differential Forms II: Riemannian Geometry Revisited [PDF]

open access: yes, 2006
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of
A. M. Vinogradov   +6 more
core   +2 more sources

Centro-affine differential geometry and the log-Minkowski problem [PDF]

open access: yesJournal of the European Mathematical Society (Print), 2021
We interpret the log-Brunn-Minkowski conjecture of B\"or\"oczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-Brunn-Minkowski operator coincides with the centro-affine Laplacian ...
E. Milman
semanticscholar   +1 more source

A quantum complexity lower bound from differential geometry [PDF]

open access: yesNature Physics, 2021
Quantum operations can be considered as points in a high-dimensional space in which distance reflects the similarity of two operations. Applying differential-geometric methods in this picture gives insights into the complexity of quantum systems ...
Adam R. Brown
semanticscholar   +1 more source

DG‐GL: Differential geometry‐based geometric learning of molecular datasets [PDF]

open access: yesInternational Journal for Numerical Methods in Biomedical Engineering, 2018
Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding ...
D. Nguyen, G. Wei
semanticscholar   +1 more source

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

open access: yesInternational Electronic Journal of Geometry, 2023
The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation of submanifolds. Later, the first author and P.
Bang‐Yen Chen   +3 more
semanticscholar   +1 more source

An Introduction to Infinite-Dimensional Differential Geometry [PDF]

open access: yes, 2021
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak ...
Alexander Schmeding
semanticscholar   +1 more source

On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric

open access: yesInternational Electronic Journal of Geometry, 2022
In this paper we introduce the Cheeger-Gromoll type metric on the coframe bundle of a Riemannian manifold and investigate the Levi-Civita connection, curvature tensor, sectional curvature and geodesics of coframe bundle with this metric.
Habil Fattayev
semanticscholar   +1 more source

The Research of Thomas P. Branson [PDF]

open access: yes, 2008
The Midwest Geometry Conference 2007 was devoted to the substantial mathematical legacy of Thomas P. Branson who passed away unexpectedly the previous year. This contribution to the Proceedings briefly introduces this legacy. We also take the opportunity
Eastwood, Michael G., Gover, A. Rod
core   +3 more sources

Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey [PDF]

open access: yes, 2008
After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of ...
Kosmann-Schwarzbach, Yvette
core   +7 more sources

Differential geometry using quaternions [PDF]

open access: yesInternational Electronic Journal of Geometry
This paper establishes the basis of the quaternionic differential geometry (HDG) initiated in a previous article. The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and torsion concepts ...
Sergio Giardino
semanticscholar   +1 more source

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