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On Some Ricci Curvature Tensors in Finsler Geometry

Mediterranean Journal of Mathematics, 2023
DAVETLİ KONUŞMACIIn this paper, we discuss several Ricci curvature tensors and their relationship with the Ricci curvature and some non-Riemannian quantities.
Zhongmin Shen, Esra Sengelen Sevim, Semail Ülgen   +2 more
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The Pressure of Ricci Curvature

Geometriae Dedicata, 2003
If \(f\: SM \to \mathbb R\) is a continuous function on the sphere bundle of a closed Riemannian manifold \((M^n,g)\), the \textit{topological pressure} \(P(f)\) is defined by \(P(f) = \sup_{\mu \in M(\Phi)} \left(h_\mu + \int_{SM} f\, d\mu\right)\), where \(M(\Phi)\) is the set of all \(\Phi\)-invariant Borel probability measures (\(\Phi\) being the ...
Paternain, Gabriel P., Petean, Jimmy
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On the Ricci curvature of steady gradient Ricci solitons [PDF]

Journal of Mathematical Analysis and Applications, 2010
Assume (Mn,g) is a complete steady gradient Ricci soliton with positive Ricci curvature. If the scalar curvature approaches 0 towards infinity, we prove that ∫0+∞Rc(γ˙(s),γ˙(s))ds=R(O), where O is the point where R obtains its maximum and γ(s) is a ...
Hongxin Guo
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A Criterion of Nonparabolicity by the Ricci Curvature

Chinese Annals of Mathematics, Series B, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Qing, Dong, Xiayu
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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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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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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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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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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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