Scalar curvature estimates by parallel alternating torsion

Scalar Curvature Estimates by Parallel Alternating Torsion

We generalize Llarull’s scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on ΛTM . As a byproduct, we show that Euler number and signature of such manifolds are determined by their global holonomy representation. Our result holds in particular for all quotients of compact Lie groups ...

Curvature Estimates in Asymptotically Flat Manifolds of Positive Scalar Curvature

Suppose that (Mn, g) is an asymptotically flat Riemannian spin manifold of positive scalar curvature. The positive mass theorem [1, 2, 3] states that the total mass of the manifold is always positive, and is zero if and only if the manifold is flat. This result suggests that there should be an inequality which bounds the Riemann tensor in terms of the total mass and implies that curvature must ...

Curvature Estimates in Asymptotically At Manifolds of Positive Scalar Curvature

Effective Gravitational “Constant” in Scalar-(Curvature)Tensor and Scalar-Torsion Gravities

In theories where a scalar field couples nonminimally to gravity, the effective gravitational “constant” becomes dependent on the value of the scalar field. This note first gives a brief review on how the cosmological evolution provides a dynamical stabilization for the gravitational “constant” as the system relaxes towards general relativity in matter dominated and potential dominated regimes ...

Prescribing Scalar Curvature on S N , Part 1 : Apriori Estimates

In this paper, we describe great details of the bubbling behavior for a sequence of solutions wi of Lwi +Riw n+2 n−2 i = 0 on S , where L is the conformal Laplacian operator of (Sn, g0) and Ri = n(n−2)+ tiR̂, R̂ ∈ C1(Sn). As ti ↓ 0, we prove among other things the location of blowup points, the spherical Harnack inequality near each blowup point and the asymptotic formulas for the interaction of ...