On the Ricci curvature of a Randers metric of isotropic S-curvature

2008 ◽  
Vol 24 (6) ◽  
pp. 911-916 ◽  
Author(s):  
Xiao Huan Mo ◽  
Chang Tao Yu
Keyword(s):  
Ricci Curvature ◽  
Randers Metric

scholarly journals Weighted projective Ricci curvature in Finsler geometry

2021 ◽  
Vol 71 (1) ◽  
pp. 183-198
Author(s):  
Tayebeh Tabatabaeifar ◽  
Behzad Najafi ◽  
Akbar Tayebi
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Randers Metric ◽  
Ricci Flat ◽  
Projectively Flat ◽  
Flat Metric ◽  
Necessary And Sufficient ◽  
Randers Metrics

Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

scholarly journals On complete Finsler spaces of constant negative Ricci curvature

2020 ◽  
Vol 17 (03) ◽  
pp. 2050041
Author(s):  
Behroz Bidabad ◽  
Maryam Sepasi
Keyword(s):  
Ricci Curvature ◽  
Schwarzian Derivative ◽  
Finsler Space ◽  
Ricci Scalar ◽  
Flag Curvature ◽  
Finsler Spaces ◽  
Randers Metric

Here, using the projectively invariant pseudo-distance and Schwarzian derivative, it is shown that every connected complete Finsler space of the constant negative Ricci scalar is reversible. In particular, every complete Randers metric of constant negative Ricci (or flag) curvature is Riemannian.

HARNACK-TYPE INEQUALITIES FOR THE POROUS MEDIUM EQUATION ON A MANIFOLD WITH NON-NEGATIVE RICCI CURVATURE

2012 ◽  
Vol 23 (04) ◽  
pp. 1250009 ◽  
Author(s):  
JEONGWOOK CHANG ◽  
JINHO LEE
Keyword(s):  
Porous Medium ◽  
Riemannian Manifold ◽  
Ricci Curvature ◽  
Porous Medium Equation ◽  
Complete Riemannian Manifold ◽  
Gradient Estimates ◽  
Medium Equation

We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.

Bounded properties of curvatures of perturbed Ricci metric on curve moduli

2014 ◽  
Vol 25 (12) ◽  
pp. 1450113
Author(s):  
Xiaorui Zhu
Keyword(s):  
Finite Volume ◽  
Ricci Curvature ◽  
Moduli Space ◽  
Point Of View ◽  
Bisectional Curvature ◽  
Bounded Geometry ◽  
Holomorphic Bisectional Curvature ◽  
Chern Form ◽  
Thick Part ◽  
Kahler Metric

As is well-known, the Weil–Petersson metric ωWP on the moduli space ℳg has negative Ricci curvature. Hence, its negative first Chern form defines the so-called Ricci metric ωτ. Their combination [Formula: see text], C > 0, introduced by Liu–Sun–Yau, is called the perturbed Ricci metric. It is a complete Kähler metric with finite volume. Furthermore, it has bounded geometry. In this paper, we investigate the finiteness of this new metric from another point of view. More precisely, we will prove in the thick part of ℳg, the holomorphic bisectional curvature of [Formula: see text] is bounded by a constant depending only on the thick constant and C0 when C ≥ (3g - 3)C0, but not on the genus g.

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