Hessian metric via transport information geometry [PDF]
Journal of Mathematics and Physics, 2020 We propose to study the Hessian metric of given functional in the space of probability space embedded with $L^2$--Wasserstein (optimal transport) metric.
Wuchen Li
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The metric geometry of singularity types [PDF]
Journal für die Reine und Angewandte Mathematik, 2019 Let X be a compact Kähler manifold. Given a big cohomology class { θ }
Tam'as Darvas, E. Nezza, Chinh H. Lu
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Kähler geometry and Chern insulators: Relations between topology and the quantum metric [PDF]
Physical review B, 2021 Bruno Mera 2, 3 and Tomoki Ozawa Instituto de Telecomunicações, 1049-001 Lisboa, Portugal Departmento de F́ısica, Instituto Superior Técnico, Universidade de Lisboa, Av.
B. Mera, T. Ozawa
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A Point-to-Distribution Joint Geometry and Color Metric for Point Cloud Quality Assessment [PDF]
IEEE International Workshop on Multimedia Signal Processing, 2021 Point clouds (PCs) are a powerful 3D visual representation paradigm for many emerging application domains, especially virtual and augmented reality, and autonomous vehicles. However, the large amount of PC data required for highly immersive and realistic
Alireza Javaheri +3 more
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Joint Geometry and Color Projection-Based Point Cloud Quality Metric [PDF]
IEEE Access, 2021 Point cloud coding solutions have been recently standardized to address the needs of multiple application scenarios. The design and assessment of point cloud coding methods require reliable objective quality metrics to evaluate the level of degradation ...
Alireza Javaheri +3 more
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On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric
International Electronic Journal of Geometry, 2023 Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with a deformed Sasaki metric. In this paper, firstly we investigate all forms of Riemannian curvature tensors of $TM$ (Riemannian curvature tensor, Ricci curvature, sectional
A. Zagane
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PFH spectral invariants on the two-sphere and the large scale geometry of Hofer’s metric [PDF]
Journal of the European Mathematical Society (Print), 2021 We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the two-sphere, equipped with Hofer's metric.
Daniel Cristofaro-Gardiner +2 more
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Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers [PDF]
SciPost Physics, 2021 Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:
B. Mera, Anwei Zhang, N. Goldman
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New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry [PDF]
Opuscula Mathematica, 2020 We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples.
D. Alpay, P. Jorgensen
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m-quasi Einstein Metric and Paracontact Geometry
International Electronic Journal of Geometry, 2022 The object of the upcoming article is to characterize paracontact metric manifolds conceding $m$-quasi Einstein metric. First we establish that if the metric $g$ in a $K$-paracontact manifold is the $m$-quasi Einstein metric, then the manifold is of ...
K. De, U. De, F. Mofarreh
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