Results 21 to 30 of about 510,591 (285)
Geometry of manifolds with area metric: multi-metric backgrounds [PDF]
, 2006 We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is ...
Arcos +35 more
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Dust content solutions for the Alcubierre warp drive spacetime
European Physical Journal C: Particles and Fields, 2020 The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive.
Osvaldo L. Santos-Pereira +2 more
doaj +1 more source
Killing tensors and a new geometric duality [PDF]
, 1995 We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor.
Bloore +20 more
core +4 more sources
Geometry-aware metric learning [PDF]
Proceedings of the 26th Annual International Conference on Machine Learning, 2009 In this paper, we introduce a generic framework for semi-supervised kernel learning. Given pair-wise (dis-)similarity constraints, we learn a kernel matrix over the data that respects the provided side-information as well as the local geometry of the data.
Zhengdong Lu +2 more
openaire +1 more source
On the Hausdorff Dimension of CAT(κ) Surfaces
Analysis and Geometry in Metric Spaces, 2016 We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls.
Constantine David, Lafont Jean-François
doaj +1 more source
F-Geometry and Amari’s α-Geometry on a Statistical Manifold
Entropy, 2014 In this paper, we introduce a geometry called F-geometry on a statistical manifold S using an embedding F of S into the space RX of random variables. Amari’s α-geometry is a special case of F-geometry.
Harsha K. V. +1 more
doaj +1 more source
Tangent Lines and Lipschitz Differentiability Spaces
Analysis and Geometry in Metric Spaces, 2016 We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves.
Cavalletti Fabio, Rajala Tapio
doaj +1 more source
A Dually Flat Embedding of Spacetime
Entropy, 2023 A model of spacetime is presented. It has an extension to five dimensions, and in five dimensions the geometry is the dual of the Euclidean geometry w.r.t. an arbitrary positive-definite metric.
Jan Naudts
doaj +1 more source
Asymptotic Geometry of the Hitchin Metric [PDF]
Communications in Mathematical Physics, 2019 We study the asymptotics of the natural $L^2$ metric on the Hitchin moduli space with group $G = \mathrm{SU}(2)$. Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore \cite{gmn13}, is that on the regular part of the Hitchin system, this metric is well-approximated by the semiflat metric from \cite{gmn13 ...
Rafe Mazzeo +3 more
openaire +3 more sources
General teleparallel metrical geometries
International Journal of Geometric Methods in Modern Physics, 2023 In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity.
Adak, Muzaffer +3 more
openaire +7 more sources