Related papers: Einstein metrics and smooth structures

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…

In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.

Let (M,J) be a minimal compact complex surface of Kaehler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a KAEHLER metric of positive scalar curvature. This extends…

Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context…

In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z_2 and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental…

We present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kaehler metrics which are toric with respect to a common 2-torus action. In the generic case, these "ambitoric" structures have an intriguing…

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can…

We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not…

We prove certain weak or idealized existence results for minimizers of the natural quadratic curvature functionals on the space of metrics on 4-manifolds. Overall, we try to exhibit the relations with the picture in 3-dimensions provided by…

On a smooth, closed Riemannian manifold $(M,g)$ of dimension $n\ge3$ with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to $g$ with constant Q-curvature of order…

This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…

Using Bochner techniques, we prove that a compact Einstein manifold of dimension $n \ge 4$ has constant curvature provided that the curvature operator of the second kind satisfies a cone condition that is strictly weaker than nonnegativity.…

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n+1)-dimensional Sasakian manifold admits a weakly Einstein metric then its scalar curvature $s$ satisfies $-6\leqslant s…

The author has elsewhere given a complete classification of those compact oriented Einstein 4-manifolds on which the self-dual Weyl curvature is everywhere positive in the direction of some self-dual harmonic 2-form. In this article,…

A method, due to \'Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant…

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…

Let (M, g, omega) be a compact, almost-Kaehler Einstein 4-manifold of negative star-scalar curvature. Then (M, omega) is a MINIMAL symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected…

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic…

Given a noncollapsing sequence of m-dimensional compact Einstein manifolds with a uniform energy bound, the Gromov-Hausdorff limit is a compact Einstein orbifold with at most finitely many singularities. Conversely, starting with a compact…

We construct infinitely many smooth oriented 4-manifolds containing pairs of homotopic, smoothly embedded 2-spheres that are not topologically isotopic, but that are equivalent by an ambient diffeomorphism inducing the identity on homology.…