Related papers: New examples of Sasaki-Einstein manifolds
We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein's equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black…
We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar…
We give a criterion for compact Sasakian manifolds to be deformed to Sasakian manifolds which are locally isomorphic to circle bundles of anti-canonical bundles over Hermitian symmetric spaces as a Sasakian analogue of Simpson's…
We focus on the classical open problem of the classification of K\"ahler-Einstein manifolds that can be K\"ahler immersed into a complex projective space endowed with the Fubini-Study metric. In particular, we will deal with such problem in…
We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of the contact bundle being trivial. This is based on Wang-Zhu's…
We construct infinitely many examples of finite volume 4-manifolds with $T^3$ ends that do not admit any cusped asymptotically hyperbolic Einstein metrics yet satisfy a strict logarithmic version of the Hitchin-Thorpe inequality due to…
The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has the…
In this paper we compute the Futaki invariant of adiabatic Kaehler classes on resolutions of Kaehler orbifolds with isolated singularities. Combined with previous existence results of extremal metrics by Arezzo-Lena-Mazzieri, this gives a…
We classify simply connected compact Sasaki manifolds of dimension $2n+1$ with positive transverse bisectional curvature. In particular, the K\"ahler cone corresponding to such manifolds must be bi-holomorphic to $\C^{n+1}\backslash \{0\}$.…
We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT,…
We use the correspondence between extremal Sasaki structures and weighted extremal Kahler metrics defined on a regular quotient of a Sasaki manifold, established by the first two authors, and Lahdili's theory of weighted K-stability in…
We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum…
It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier…
We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric…
In this note, we construct new examples of Lorentzian Sasaki-Einstein (LSE) metrics on Smale manifolds $M.$ It has already been established in \cite{Gmz2} that such metrics exist on the so-called torsion free Smale manifolds, i.e. the…
We relate the global log canonical threshold of a variety with torus action to the global log canonical threshold of its quotient. We apply this to certain Fano varieties and use Tian's criterion to prove the existence of Kahler-Einstein…
We obtain infinite classes of new Einstein-Sasaki metrics on complete and non-singular manifolds. They arise, after Euclideanisation, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces…
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 give a new proof of the fact that the condition of a Fano manifold admitting a K\"ahler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability.…
We study null Sasakian structures in dimension five. First, based on a result due to Koll\'ar [Ko], we improve a result by Boyer, Galicki and Matzeu in [BGM] and prove that simply connected manifolds diffeomorphic to $# k(S^2\times S^3)$…