Related papers: A Note on Einstein Sasaki Metrics in D \ge 7

We study the question of the existence of left-invariant Sasaki contact structures on the seven-dimensional nilpotent Lie groups. It is shown that the only Lie group allowing Sasaki structure with a positive definite metric tensor is the…

On $4$-symmetric symplectic spaces, invariant almost complex structures -- up to sign -- arise in pairs. We exhibit some $4$-symmetric symplectic spaces, with a pair of "natural" compatible (usually not positive) invariant almost complex…

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a…

By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm…

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to…

Motivated by the work of Li and Mantoulidis, we study singular metrics which are uniformly Euclidean $(L^\infty)$ on a compact manifold $M^n$ ($n\ge 3$) with negative Yamabe invariant $\sigma(M)$. It is well-known that if $g$ is a smooth…

We initiate a systematic study of the deformation theory of the second Einstein metric $g_{1/\sqrt{5}}$ respectively the proper nearly $G_2$ structure $\varphi_{1/\sqrt{5}}$ of a $3$-Sasaki manifold $(M^7,g)$. We show that infinitesimal…

We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersymmetric AdS_5…

Generalized $(\kappa ,\mu )$ structures occur in dimension 3 only. In this dimension 3, only K-contact structures can occur as generalized Eta-Einstein. On closed manifolds, Eta-Einstein, K-contact structures which are not D-homothetic to…

We consider supergravity in five-dimensional Anti-De Sitter space $AdS_{5}$ with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $M$. Our main result reveals how the Sasaki-Einstein metric…

The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…

Let $(M,g)$ be an $n-$dimensional Riemannian manifold and $T_{1}^{1}(M)$ be its $(1,1)-$tensor bundle equipped with the rescaled Sasaki type metric $% ^{S}g_{f}$ which rescale the horizontal part by a nonzero differentiable function $f$. In…

We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci…

In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct…

Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking…

We show that the moduli space of simple flat bundles over a compact Sasakian manifold is a finite disjoint union of moduli spaces of simple flat bundles with fixed basic structures. This gives a detailed description of the non-abelian Hodge…

Proper conformal symmetries in self-dual (SD) Einstein spaces are considered. It is shown, that such symmetries are admitted only by the Einstein spaces of the type [N]x[N]. Spaces of the type [N]x[-] are considered in details. Existence of…

In earlier work we have shown that for certain geometric structures on a smooth manifold $M$ of dimension $n$, one obtains an almost para-K\"ahler--Einstein metric on a manifold $A$ of dimension $2n$ associated to the structure on $M$. The…

We answer in the affirmative the question posed by Conti and Rossi on the existence of nilpotent Lie algebras of dimension 7 with an Einstein pseudo-metric of nonzero scalar curvature. Indeed, we construct a left-invariant pseudo-Riemannian…

No! We show that the field equations of Einstein-Gauss-Bonnet theory defined in generic $D>4$ dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to $D=4$.…