Related papers: Compact weak G_2-manifolds with conical singularit…

An important open question in G$_{2}$ geometry concerns whether or not a compact seven-manifold can support an exact G$_{2}$-Structure. Given the significance of this question we initiate a study of exact G$_{2}$-Structures on compact…

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to…

For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of…

There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\varphi,*\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\omega)$. We can also generalize $(X,\varphi,*\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\varphi,\psi)$,…

The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. In a previous paper (Invent. math. 123 (1996), 507-552) the author constructed the first examples of compact 8-manifolds with holonomy Spin(7), by…

We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map…

We classify $7$-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in $\mathrm{G}_2$, up to naturally reductive homogeneous spaces and nearly parallel…

In this paper, a metric with G$_2$ holonomy and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the flag manifold.

We study existence problems for closed $G_2$-structures with negative Ricci curvature, and we prove the $G_2$-Goldberg conjecture for noncompact manifolds. We first show that no closed manifold admits a closed $G_2$-structure with negative…

This paper gives a uniform, self-contained and direct approach to a variety of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give necessary and sufficient cohomological criteria for the existence of various…

This is the first nontrivial construction to date of instantons over a compact manifold with holonomy exactly $G_2$. The HYM connections on asymptotically stable bundles over Kovalev's noncompact Calabi-Yau 3-folds, obtained in the first…

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…

We study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss-Bonnet and signature theorems for arbitrary…

Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n \ge 5$ and…

We study Ricci-flat metrics on non-compact manifolds with the exceptional holonomy $Spin(7), G_2$. We concentrate on the metrics which are defined on ${\bf R} \times G/H$. If the homogeneous coset spaces $G/H$ have weak $G_2$, SU(3)…

We study complete, simply-connected manifolds with special holonomy that are toric with respect to their multi-moment maps. We consider the cases where there is a connected non-Abelian symmetry group containing the torus. For…

For a compact connected Lie group $G$ acting as isometries on a compact orientable Riemannian manifold $M^{n+1},$ and cohomogeneity not equal to 0 or 2, we prove the existence of a nontrivial embedded $G$-invariant minimal hypersurface,…

Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that a compact and connected Lie group $G$ acts on $M$ in a Hamiltonian manner, and that this action linearizes to $A$. Then there is an associated unitary…

We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in $\mathbb{C}^2$ with cone singularities along a smooth complex curve. These metrics are expected to arise as blow up limits of non collapsed sequences of…

The condition of having an $N=1$ spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been…