Related papers: Quasi-Einstein metrics on sphere bundles
In this paper we study the set of balanced metrics (in Donaldson's terminology) on a compact complex manifold M which are homothetic to a given balanced one. This question is related to various properties of the Tian-Yau-Zelditch…
We numerically calculate Perelman's entropy for a variety of canonical metrics on $\mathbb{CP}^{1}$-bundles over products of Fano K\"ahler-Einstein manifolds. The metrics investigated are Einstein metrics, K\"ahler-Ricci solitons and…
A twisted Higgs bundle on a K\"ahler manifold $X$ is a pair $(E,\phi)$ consisting of a holomorphic vector bundle $E$ and a holomorphic bundle morphism $\phi\colon M\otimes E \to E$ for some holomorphic vector bundle $M$. Such objects were…
We examine various examples of horosymmetric manifolds which exhibit interesting properties with respect to canonical metrics. In particular, we determine when the blow-up of a quadric along a linear subquadric admits K\"ahler-Einstein…
In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the $m$-Quasi Einstein…
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in…
We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, under Q-Gorenstein smoothings.
We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…
We prove a generic spin-statistics relation for the fractional quasiparticles that appear in abelian quantum Hall states on the disk. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle…
An ansatz of Calabi allows construction of Kahler metrics in an Hermitian disk bundle over a Kahler manifold. We attempt to give a definitive treatment of this ansatz, with the following results: We give curvature conditions on the disk…
We find the necessary conditions for a sequential warped product manifold to be a quasi-Einstein manifold. We also investigate the necessary and sufficient conditions for a sequential standard static space-time and a sequential generalized…
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian…
We show that if a Fano manifold $M$ is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then $M$ admits a K\"ahler-Einstein metric. This is a strengthening of the solution of the…
In this short note we are concerned with the Kahler-Einstein metrics near cone type log canonical singularities. By two different approaches, we construct a complete Kahler-Einstein metric with negative scalar curvature in a neighborhood of…
We prove that compact K\"ahler manifolds whose sectional curvatures are close to 1/4-pinched have ratios of Chern numbers close to the corresponding ratios of a complex hyperbolic space form. We deduce that the Mostow-Siu surfaces (and…
We consider sphere bundles P and P' of totally null planes of maximal dimension and opposite self-duality over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP' of P and P' is found to be…
This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…
We consider quasifuchsian manifolds with "particles", i.e., cone singularities of fixed angle less than $\pi$ going from one connected component of the boundary at infinity to the other. Each connected component of the boundary at infinity…
The purpose of this paper is twofold. First we study a class of Banach manifolds which are not differentiable in traditional sense but they are quasi-differentiable in the sense that a such Banach manifold has an embedded submanifold such…