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Information geometry

Japanese journal of mathematics, 2021
Information geometry has emerged from the study of the invariant structure in families of probability distributions. This invariance uniquely determines a second-order symmetric tensor g and third-order symmetric tensor T in a manifold of probability ...
S. Amari
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Pure Metric Geometry

SpringerBriefs in Mathematics, 2020
We discuss only domestic affairs of metric spaces, leaving all external applications aside. Topics include universal spaces, injective spaces, Gromov--Hausdorff convergence, and ultralimits.
A. Petrunin
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On the geometry of the tangent bundle with vertical rescaled generalized Cheeger-Gromoll metric

, 2020
Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle TM . We calculate its Levi-
L. Belarbi, H. E. Hendi, F. Lattı
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Connection between non-metric differential geometry and mathematical theory of imperfections

International Journal of Engineering Science, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research

Transactions of the Moscow Mathematical Society, 2016
The paper is devoted to the presentation of researches on geometry in the Moscow Mathematical Society. Geometry is meant here in a broader sense. The material is organized into the following subjects: manifolds with a metric, in particular manifolds with a Riemannian metric or Riemannian spaces, isometric realizations of abstract metrics as metrics of ...
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Complexity of distances: Reductions of distances between metric and Banach spaces

Israel Journal of Mathematics, 2020
We show that all the standard distances from metric geometry and functional analysis, such as Gromov—Hausdorff distance, Banach—Mazur distance, Kadets distance, Lipschitz distance, Net distance, and Hausdorff—Lipschitz distance have all the same ...
Marek C'uth, M. Doucha, O. Kurka
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