Results 1 to 10 of about 7,336 (96)

Linearization of nonlinear connections on vector and affine bundles, and some applications [PDF]

Journal of Physics A: Mathematical and Theoretical, 2018
A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization and restriction. Several applications in Classical Mechanics are provided.
Eduardo Martínez
semanticscholar   +8 more sources

Geometries involving affine connections and general linear connections [PDF]

Annali di Matematica Pura ed Applicata, 1934
This paper deals with a general linear connection in the sense of R. König, in which a space of \(m\) dimensions is attached to each point of a general manifold of \(n\) dimensions. In such a general manifold of \(n\) dimensions are assumed a symmetric linear connection \(\Gamma_{jk}^i\), and a general linear connection \(L_{\beta a}^\alpha\), both ...
Michal, A. D., Botsford, J. L.
semanticscholar   +3 more sources

Linear transformations on affine-connections [PDF]

Classical and quantum gravity, 2020
We state and prove a simple theorem that allows one to generate invariant quantities in metric-affine geometry, under a given transformation of the affine connection.
Damianos Iosifidis
openalex   +3 more sources

Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type

Differential Geometry of Manifolds of Figures, 2021
The theory of tangent bundles over a differentiable manifold M be­longs to the geometry and topology of manifolds and is an intensively developing area of the theory of fiber spaces. The foundations of the theo­ry of fibered spaces were laid in the works
A. Ya. Sultanov, G.A. Sultanova, N.V. Sadovnikov   +2 more
openalex   +2 more sources

Simultaneous Differential Invariants of an Affine Connection and a General Linear Connection [PDF]

Proceedings of the National Academy of Sciences, 1932
Michal, A. D., Botsford, J. L.
openaire   +5 more sources

Heaps of Linear Connections and Their Endomorphism Truss [PDF]

Symmetry, 2023
We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold.
A. Bruce
semanticscholar   +1 more source

Linear and projective connections over a smooth manifold

Differential Geometry of Manifolds of Figures, 2023
The principal bundles of the first order coframes and the second order coframes, as well as factor bundle of centroprojective (coaffine) coframes are considered.
Y. Shevchenko, A. V. Vyalova
semanticscholar   +1 more source

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

Mathematics, 2021
In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces.
V. Berezovski, Yevhen Cherevko, J. Mikeš, L. Rýparová   +3 more
semanticscholar   +1 more source

Errors Dynamics in Affine Group Systems [PDF]

arXiv.org, 2023
Errors dynamics captures the evolution of the state errors between two distinct trajectories, that are governed by the same system rule but initiated or perturbed differently.
Xing Li, Jianqi Chen, Han Zhang, Jieqiang Wei, Junfeng Wu   +4 more
semanticscholar   +1 more source

Exactly solvable connections in metric-affine gravity [PDF]

Classical and quantum gravity, 2018
This article presents a systematic way to solve for the affine connection in metric-affine geometry. We start by adding to the Einstein–Hilbert action, a general action that is linear in the connection and its partial derivatives and respects projective ...
D. Iosifidis
semanticscholar   +1 more source