Related papers: Improved Estimates for $G_2$-structures on the Gen…
We study the natural G_2 structure on the unit tangent sphere bundle SM of any given orientable Riemannian 4-manifold M, as it was discovered in \cite{AlbSal}. A name is proposed for the space. We work in the context of metric connections,…
We propose a method to construct G_2-instantons over a compact twisted connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end (see arXiv:1310.7933). In our…
We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is…
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' $(X,\varphi,\psi)$,…
We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian…
Interest in Riemannian manifolds with holonomy equal to the exceptional Lie group $\mathrm{G}_2$ have spurred extensive research in geometric flows of $\mathrm{G}_2$-structures defined on seven-dimensional manifolds in recent years. Among…
We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion…
We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…
This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as…
We study natural variations of the G2 structure {\sigma}_0 \in {\Lambda}^3_+ existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M. We find a circle of structures for which the induced metric is the usual…
This is a survey paper. We explain the known constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy G2. One method uses resolutions of singularities of appropriately chosen…
We describe the second order obstruction to deformation for nearly $G_2$ structures on compact manifolds. Building on work of B.Alexandrov and U.Semmelmann this allows proving rigidity under deformation for the proper nearly $G_2$ structure…
In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…
Inspired by a string duality, we construct a deformation family for $G_2$-orbifolds given as total spaces of coassociative fibrations by ADE singularities over a closed and oriented smooth three-manifold $Q$. The deformations are…
This paper proves a general collapsing result for families of stratified Riemannian metrics $\widehat{g}^\mu$ on a compact orbifold $E$, subject to suitable limiting conditions on the metrics $\widehat{g}^\mu$ as $\mu \to \infty$. The…
We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted…
The goal of this paper is the construction of a compact manifold with G$_2$ holonomy and nodal singularities along circles using twisted connected sum method. This paper finds matching building blocks by solving the Calabi conjecture on…
We study the infinitesimal deformations of a proper nearly parallel G_2-structure and prove that they are characterized by a certain first order differential equation. In particular we show that the space of infinitesimal deformations…
The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional…
We exhibit examples of closed Riemannian 7-manifolds with holonomy G_2 such that the underlying manifolds are diffeomorphic but whose associated G_2-structures are not homotopic. This is achieved by defining two invariants of certain…