Related papers: New Einstein Metrics on 8#(S^2 times S^3)

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat…

We prove the existence of multiparameter isospectral deformations of metrics on SO(n) $(n = 9$ and $n\geq 11)$, SU(n) $(n\geq 8)$, and $Sp(n)$ $(n\geq 4)$. For these examples, we follow a metric construction developed by Schueth who had…

In this article, we prove that every compact simple Lie group $SO(n)$ for $n\geq 10$ admits at least $2\left([\frac{n-1}{3}]-2\right)$ non-naturally reductive left-invariant Einstein metrics.

Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous five-dimensional Einstein-Sasaki space Y^{2,1} was obtained. It was constructed by specialising the parameters in the BPS limit of recently-discovered…

Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate…

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

In this expository article we review the problem of finding Einstein metrics on compact K\"ahler manifolds and Sasaki manifolds. In the former half of this article we see that, in the K\"ahler case, the problem fits better with the notion…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

We study existence of invariant Einstein metrics on complex Stiefel manifolds $G/K = \SU(\ell+m+n)/\SU(n) $ and the special unitary groups $G = \SU(\ell+m+n)$. We decompose the Lie algebra $\frak g$ of $G$ and the tangent space $\frak p$ of…

We study the existence of projectable $G$-invariant Einstein metrics on the total space of $G$-equivariant fibrations $M=G/L\to G/K$, for a compact connected semisimple Lie group $G$. We obtain necessary conditions for the existence of such…

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal…

We construct isospectral pairs of Riemannian metrics on S^5 and on B^6, thus lowering by three the dimension of spheres and balls on which such metrics have been constructed previously (S^{n\ge 8} and B^{n\ge 9}). We also construct…

We prove that any simply connected compact 3-Sasakian manifold, of dimension seven, is formal if and only if its second Betti number is $b_2<2$. In the opposite, we show an example of a 7-dimensional Sasaki-Einstein manifold, with second…

We find the precise number of non-K\"ahler $SO(2n)$-invariant Einstein metrics on the generalized flag manifold $M=SO(2n)/U(p)\times U(n-p)$ with $n\geq 4$ and $2\leq p\leq n-2$. We use an analysis on parametric systems of polynomial…

A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures…

It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After reviewing subsequent progress that has been made on this topic,…

This paper presents a systematic study of invariant Einstein metrics on basic classical Lie supergroups, whose Lie superalgebras belong to the Kac's classification of finite dimensional classical simple Lie superalgebras over $\mathbb{R}$.…

We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal…

In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$…

We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of…