Results 1 to 10 of about 99,178 (163)
On the Non Metrizability of Berwald Finsler Spacetimes [PDF]
Universe, 2020 We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund ...
Andrea Fuster +3 more
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Affine Connection Representation of Gauge Fields [PDF]
Advances in High Energy Physics, 2022 There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection.
Zhao-Hui Man
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Quadratic metric-affine gravity: solving for the affine-connection
European Physical Journal C: Particles and Fields, 2022 We consider the most general 11 parameter parity even quadratic Metric-Affine Theory whose action consists of the usual Einstein–Hilbert plus the 11 quadratic terms in torsion, non-metricity as well as their mixing.
Damianos Iosifidis
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Affine connections and second-order affine structures
, 2020 Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure of an ...
Bár, Filip
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Note on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Recently Cherednik and Feigin [arXiv:1209.1978] obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA).
Tomoki Nakanishi
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Two Invariants for Geometric Mappings
Axioms, 2022 Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants.
Nenad O. Vesić +2 more
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Examples of non-flat bundles of rank one
Comptes Rendus. Mathématique, 2023 It is expected that there exist line bundles on a quasi-affine non-singular surface which do not admit a flat connection. However, to the best of our knowledge there is no known example of such a line bundle.
Dan, Ananyo, Romano-Velázquez, Agustín
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About the torsion tensor of an affine connection on two-dimensional and three-dimensional manifolds
Дифференциальная геометрия многообразий фигур, 2021 The basis for this study of affine connections in linear frame bundle over a smooth manifold is the structure equations of the bundle. An affine connection is given in this bundle by the Laptev — Lumiste method. The differential equations are written for
K.V. Polyakova
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Aspects of the polynomial affine model of gravity in three dimensions
European Physical Journal C: Particles and Fields, 2022 The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently ...
Oscar Castillo-Felisola +5 more
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The Berwald-type linearisation of generalised connections [PDF]
, 2003 We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of ...
Bejancu A +24 more
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