Characterization of null cones under a Ricci curvature condition

2021 ◽  
pp. 125906
Author(s):  
Manuel Gutiérrez ◽  
Benjamín Olea
Keyword(s):  
Ricci Curvature ◽  
Curvature Condition

A note on a three-dimensional sphere theorem with integral curvature condition

2016 ◽  
Vol 18 (04) ◽  
pp. 1550070 ◽  
Author(s):  
Mijia Lai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Integral Curvature ◽  
Spherical Space ◽  
Sphere Theorem ◽  
Curvature Condition ◽  
Spherical Space Form

In this paper, we obtain a three-dimensional sphere theorem with integral curvature condition. On a closed three manifold [Formula: see text] with constant positive scalar curvature, if a certain combination of [Formula: see text] norm of the Ricci curvature and [Formula: see text] norm of the scalar curvature is positive, then [Formula: see text] is diffeomorphic to a spherical space form.

scholarly journals Characterization of Pinched Ricci Curvature by Functional Inequalities

2017 ◽  
Vol 28 (3) ◽  
pp. 2312-2345 ◽  
Author(s):  
Li-Juan Cheng ◽  
Anton Thalmaier
Keyword(s):  
Ricci Curvature ◽  
Functional Inequalities

scholarly journals Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound

2018 ◽  
Vol 72 (1) ◽  
pp. 243-280
Author(s):  
Yohei Sakurai
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Suitable Condition ◽  
Manifolds With Boundary ◽  
Weighted Mean ◽  
Curvature Condition ◽  
Curvature Bound ◽  
Comparison Geometry ◽  
Weighted Mean Curvature ◽  
Weighted Ricci Curvature

AbstractWe study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.

scholarly journals On interpolation and curvature via Wasserstein geodesics

2017 ◽  
Vol 10 (2) ◽  
pp. 125-167 ◽  
Author(s):  
Martin Kell
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorem ◽  
Similar Condition ◽  
Interpolation Inequality ◽  
Metric Measure Spaces ◽  
Main Ingredient ◽  
Curvature Condition ◽  
Finsler Manifolds ◽  
Measure Spaces ◽  
Positively Curved

AbstractIn this article, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel–Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott–Villani and Sturm to define an abstract Ricci curvature condition. Following their ideas, a similar condition can be defined and for positively curved spaces one can prove a Poincaré inequality. Using Gigli’s recently developed calculus on metric measure spaces, even a q-Laplacian comparison theorem holds on q-infinitesimal convex spaces. In the appendix, the theory of Orlicz–Wasserstein spaces is developed and necessary adjustments to prove the interpolation inequality along geodesics in those spaces are given.

Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes

1978 ◽  
Vol 84 (1) ◽  
pp. 159-175 ◽  
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich
Keyword(s):  
Ricci Curvature ◽  
Energy Condition ◽  
Cauchy Surface ◽  
Energy Conditions ◽  
Curvature Condition ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Dimension 2 ◽  
Hyperbolic Spacetimes ◽  
Conformal Deformations

AbstractWe consider globally hyperbolic spacetimes (M, g) of dimension ≥ 3 satisfying the curvature condition Ric (g) (v, v) ≥ 0 for all non-spacelike tangent vectors v in TM. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M, g) admits a smooth globally hyperbolic time function h: M → such that for some t0, the Cauchy surface h−1(t0) satisfies the strict curvature condition Ric (g) (v, v) > 0 for all non-spacelike v attached to h−1(t0). Then M admits a metric g′ conformal to g satisfying the strict curvature condition Ric (g′) (v, v) > 0 for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension ≥ 2 and for non-positive Ricci curvature.

Almost Ricci solitons isometric to spheres

2019 ◽  
Vol 16 (05) ◽  
pp. 1950073 ◽  
Author(s):  
Sharief Deshmukh
Keyword(s):  
Lower Bound ◽  
Poisson Equation ◽  
Ricci Curvature ◽  
Unit Sphere ◽  
Potential Field ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Almost Ricci Soliton

We find a characterization of a sphere using a compact gradient almost Ricci soliton and the lower bound on the integral of Ricci curvature in the direction of potential field. Also, we use Poisson equation on a compact gradient almost Ricci soliton to find a characterization of the unit sphere.

Constructions of Einstein Finsler metrics by warped product

2018 ◽  
Vol 29 (11) ◽  
pp. 1850081 ◽  
Author(s):  
Bin Chen ◽  
Zhongmin Shen ◽  
Lili Zhao
Keyword(s):  
Ricci Curvature ◽  
Warped Product ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Product Structures

The warped product structures of Finsler metrics are studied in this paper. We give the formulae of the flag curvature and Ricci curvature of these metrics, and obtain the characterization of such metrics to be Einstein. Some Einstein Finsler metrics of this type are constructed.

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