Results 211 to 220 of about 71,420 (241)

Riemann Curvature and Ricci Curvature

2012
Curvatures are the central concept in geometry. The notion of curvature introduced by B. Riemann faithfully reveals the local geometric properties of a Riemann metric. This curvature is called the Riemann curvature in Riemannian geometry. The Riemann curvature can be extended to Finsler metrics as well as the sectional curvature.
Xinyue Cheng, Zhongmin Shen
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Ricci Curvature and Fundamental Group*

Chinese Annals of Mathematics, Series B, 2006
Let \(M\) be a compact Riemannian manifold with negative Ricci curvature. The author shows that if the universal cover of \(M\) has a pole and if any geodesic sphere centered at the pole is convex or concave, then the growth function of the fundamental group is at least exponential.
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Metrics of Negative Ricci Curvature

The Annals of Mathematics, 1994
Using some deformation techniques the author is able to construct Riemannian metrics \(g\) of negative Ricci curvature \(r(g)\) and to prove in this way the following remarkable results: (i) For any \(n \geq 3\) there exist constants \(a(n) > b(n) > 0\) such that any manifold \(M\) with \(\dim M \geq 3\) admits a complete Riemannian metric \(g\) for ...
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Graphs with Positive Ricci Curvature

Graphs and Combinatorics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiqi Huang, Weihua He, Chaoqin Zhang
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On the Ricci curvature of a Randers metric of isotropic S-curvature

Acta Mathematica Sinica, English Series, 2008
An \(n\)-dimensional compact manifold \(M\) is considered with a Randers metric \(F=\alpha+\beta\) and with constant \(c\) isotropic \(S\)-curvature i.e. having the form \(\mathcal S(x,y)=(n+1)c F(x,y)\). A number of Finsler manifolds of isotropic \(\mathcal S\)-curvature were given by the first author and \textit{C. Yang} [Differ. Geom. Appl.
Mo, Xiaohuan, Yu, Changtao
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Ricci Curvature and Volume Convergence

The Annals of Mathematics, 1997
The author gives a new integral estimate of distances and angles on manifolds with a given lower Ricci curvature bound. He obtains this estimate via a Hessian estimate and states it in three different forms. Using this, he proves (among other things) the following conjectures: 1.
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The Ricci Curvature

1998
In this chapter we deal with problems concerning Ricci Curvature mainly: Prescribing the Ricci curvature Ricci curvature with a given sign Existence of Einstein metrics.
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On the Ricci curvature of Kähler-Ricci flow

2022
In this thesis, we consider n-dimensional compact Kähler manifold X with semi-ample canonical line bundle. We investigate the bound of Ricci curvature of X along the long time solution of Kähler Ricci Flow. In particular, when the fibres of X over the canonical model X can of X are biholomorphic to each other and the Kodaira dimension ...
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Weighted Ricci Curvature

2021
In Part I, we saw that the natural notions of Finsler curvatures (the flag and Ricci curvatures) can be introduced through the behavior of geodesics, and then several comparison theorems follow smoothly by similar arguments to the Riemannian case, or through the characterizations of these curvatures from the Riemannian geometric point of view.
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Ricci curvature and measures

Japanese Journal of Mathematics, 2009
This article is based on the 5th Takagi Lectures delivered by Jean-Pierre Bourguignon at the University of Tokyo on October 4 and 5, 2008. It offers the general reader -- even those of us not steeped in Differential Geometry -- a fascinating glimpse and interesting account of the development, during the last thirty years, of the analysis of spaces ...
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