Related papers: Some remarks on Einstein-Randers metrics
In K-stability, the delta invariant of a Fano variety encodes the existence of K\"ahler-Einstein metrics. We introduce a weighted analytic delta invariant, and a reduced version, that characterize the existence of weighted solitons. We…
Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a K\"ahler metric with cone angle $2\pi\beta$ along $D$ which has bounded Ricci…
It is well-known that the Einstein condition on warpedgeometries requires the fibres to be necessarily Einstein. However, exact warped solutions have often been obtained using one- and two-dimensional bases. In this paper, keeping the…
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms of…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…
The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning ({\alpha}, \beta})-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this…
Quasi-Einstein manifolds are well-studied generalizations of Einstein manifolds. This includes gradient Ricci solitons and has a natural correspondence with the warped product Einstein manifolds. A quasi-Einstein metric is said to be rigid…
We prove linear semi-stability for a large class of Einstein metrics of non-positive scalar curvature. More precisely, we show that any Einstein $n$-manifold with non-positive scalar curvature carrying a parallel twisted pure spin$^r$…
In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian…
In this paper, we study the reversibility of Riemann curvature and Ricci curvature for the Matsumoto metric and prove three global results. First, we prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic. Then we…
In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing…
We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature.…
In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a…
It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the…
Suppose $M$ is a manifold with boundary. Choose a point $o\in\partial M$. We investigate the prescribed Ricci curvature equation $\Ric(G)=T$ in a neighborhood of $o$ under natural boundary conditions. The unknown $G$ here is a Riemannian…
We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kahler metrics with zero scalar curvature, and metrics…
In this paper, we study general $(\alpha,\beta)$-metrics which $\alpha$ is a Riemannian metric and $\beta$ is an one-form. We have proven that every weak Landsberg general $(\alpha,\beta)$-metric is a Berwald metric, where $\beta$ is a…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…