Related papers: Invariant Einstein metrics on real flag manifolds …

This paper investigates the failure of certain metric measure spaces to be infinitesimally Hilbertian or quasi-Riemannian manifolds, by constructing examples arising from a manifold $M$ endowed with a Riemannian metric $g$ that is possibly…

We characteristize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisty certain characterisitc…

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly…

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

We give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4-manifolds $(X_k)$ previously…

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…

We present a pair of open smooth $4$-manifolds that are mutually homeomorphic. One of them admits a Riemannian metric that possesses quasi-cylindricity, and positivity of scalar curvature and of dimension of certain $L^2$ harmonic forms. By…

A nilsoliton is a nilpotent Lie algebra $\mathfrak{g}$ with a metric such that $\operatorname{Ric}=\lambda \operatorname{Id}+D$, with $D$ a derivation. For indefinite metrics, this determines four different geometries, according to whether…

In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$.…

Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds…

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…

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with…

We show that a combination of collapsing and excessive growth from the fundamental group impedes the existence of Einstein metrics on several families of smooth four-manifolds. These include infrasolvmanifolds whose fundamental group is not…

With a f-left-invariant Riemannian metric on a Lie group $G$, we mean a Riemannian metric which is conformally equivalent to a left-invariant Riemannian metric, with the conformal factor $f$. In this article, we study the geometry of such…

One says that a Riemannian four-manifold is \emph{weakly Einstein} if the three-index contraction of its curvature tensor against itself equals a function times the metric. Since this includes all four-manifolds that are Einstein, or…

We prove local polyhomogeneity of asymptotically real or complex hyperbolic Einstein metrics, with application to unique continuation problems.

In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension…

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum…

We study locally conformal calibrated $G_2$-structures whose underlying Riemannian metric is Einstein, showing that in the compact case the scalar curvature cannot be positive. As a consequence, a compact homogeneous $7$-manifold cannot…

We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers.…