Related papers: Einstein metrics and GIT stability

In this work we study the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic…

We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary…

Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so…

Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool…

We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse…

It is well known that every compact simple Lie group G admits an Einstein metric that is invariant under the independent left and right actions of G. In addition to this bi-invariant metric, with G x G symmetry, it was shown by D'Atri and…

We introduce a holomorphic sheaf E on a Sasaki manifold and study two new notions of stability for E along the Sasaki-Ricci flow related to the `jumping up' of the number of global holomorphic sections of E at infinity. First, we show that…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

In this paper, we introduce the notions of slope stability and the Hermitian Einstein metric for big cohomology classes. The main result is the Kobayashi Hitchin correspondence on compact normal spaces with big classes admitting the…

Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C…

This paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics. Firstly, we reduce the geodesic equation in the space of Sasakian metrics to a Dirichlet problem of degenerate complex Monge-Amp\'ere…

We point out a simple construction of an infinite class of Einstein near-horizon geometries in all odd dimensions greater than five. Cross-sections of the horizons are inhomogeneous Sasakian metrics (but not Einstein) on S^3xS^2 and more…

We propose new types of canonical metrics on K\"ahler manifolds, called coupled K\"ahler-Einstein metrics, generalizing K\"ahler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and…

The aim of this paper is to construct infinitely many families of Einstein metrics on the connected sums of arbitrary number of copies of $S^2\times S^3$. We realize these 5-manifolds as total spaces of Seifert bundles over Del Pezzo…

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove…

In the probabilistic construction of K\"ahler-Einstein metrics on a complex projective algebraic manifold X - involving random point processes on X - a key role is played by the partition function. In this work a new quantitative bound on…

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on…

Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations,…

In this short note, we prove that a Calabi extremal Kaehler-Ricci soliton on a compact toric Kaehler manifold is Einstein. This solves for the class of toric manifolds a general problem stated by the authors that they solved only under some…

The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…