Results 11 to 20 of about 409,873 (273)
On the projective Ricci curvature [PDF]
Science China Mathematics, 2020 The notion of the Ricci curvature is defined for sprays on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. In this paper,
Z. Shen, Liling Sun
semanticscholar +5 more sources
Ricci curvature of submanifolds in Kenmotsu space forms [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension.
Kadri Arslan +4 more
doaj +2 more sources
Introducing quantum Ricci curvature [PDF]
Physical Review D, 2017 Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by ...
N. Klitgaard, R. Loll
semanticscholar +6 more sources
Ricci curvature for metric-measure spaces via optimal transport [PDF]
, 2004 We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R.
John Lott, Cédric Villani
openalex +3 more sources
Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
doaj +2 more sources
Implementing quantum Ricci curvature [PDF]
Physical Review D, 2018 Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure.
N. Klitgaard, R. Loll
semanticscholar +5 more sources
The equation of prescribed Ricci curvature [PDF]
Bulletin of the American Mathematical Society, 1980 Dennis DeTurck
openalex +4 more sources
On $m$-th root metrics of isotropic projective Ricci curvature [PDF]
AUT Journal of Mathematics and Computing, 2023 The Ricci curvature is introduced by spray on $M^n$. Sprays are deformed to projective sprays with a volume form $dV$ on $M^n$. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays.
Mehran Gabrani +2 more
doaj +1 more source
Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature [PDF]
LOG IN, 2023 While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently.
Lukas Fesser, Melanie Weber
semanticscholar +1 more source
Revisiting Over-smoothing and Over-squashing using Ollivier's Ricci Curvature [PDF]
International Conference on Machine Learning, 2022 Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking ...
K. Nguyen +5 more
semanticscholar +1 more source