Related papers: SU(4)-holonomy via the left-invariant hypo and Hit…

We investigate left-invariant Hitchin and hypo flows on $5$-, $6$- and $7$-dimensional Lie groups. They provide Riemannian cohomogeneity-one manifolds of one dimension higher with holonomy contained in $SU(3)$, $G_2$ and $Spin(7)$,…

One way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo evolution flow. In this paper we classify invariant hypo SU(2)-structures on nilpotent…

The group Spin(7) belongs to the list of possible holonomy of an eight-dimensional Riemannian manifold. The weaker notion of Spin(7)-structures plays for manifolds with holonomy Spin(7), the analogue of almost Hermitian for K{\"a}hler…

We study the moduli space of SU(3) structure manifolds X that form the internal compact spaces in four-dimensional N=1/2 domain wall solutions of heterotic supergravity with flux. Together with the direction perpendicular to the…

It was proven by Hitchin that any solution of his evolution equations for a half-flat SU(3)-structure on a compact six-manifold M defines an extension of M to a seven-manifold with holonomy in G_2. We give a new proof, which does not…

The Iwasawa manifold is uplifted to seven-folds of either G_2 holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G_2 manifold through "size" deformation…

In this short supplement to [1], we discuss the uplift of half-flat six-folds to Spin(7) eight-folds by fibration of the former over a product of two intervals. We show that the same can be done in two ways - one, such that the required…

The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on exceptional holonomy, in two parts. Part I introduces the…

Cocalibrated G_2-structures are structures naturally induced on hypersurfaces in Spin(7)-manifolds. Conversely, one may start with a seven-dimensional manifold M endowed with a cocalibrated G_2-structure and construct via the Hitchin flow a…

We develop a new construction of complete non-compact 8-manifolds with Riemannian holonomy equal to $\operatorname{Spin}(7)$. As a consequence of the holonomy reduction, these manifolds are Ricci-flat. These metrics are built on the total…

Any irreducible Dynkin diagram $\Delta$ is obtained from an irreducible Dynkin diagram $\Delta_h$ of type $\mathrm{ADE}$ by folding via graph automorphisms. For any simple complex Lie group $G$ with Dynkin diagram $\Delta$ and compact…

Four subriemannian (SR) structures over the Euclidean sphere $\mathbb{S}^7$ are considered in accordance to the previous literature. The defining bracket generating distribution is chosen as the horizontal space in the Hopf fibration, the…

This paper initiates a classification programme of flows of $\mathrm{SU}(2)$-structures on $4$-manifolds which have short-time existence and uniqueness. Our approach adapts a representation-theoretic method originally due to Bryant in the…

Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are determined and their types are characterized in terms of the shape operator and the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084} and…

Hitchin shows that half-flat SU(3)-structures on a 6-dimensional manifold M can be lifted to parallel G_{2}-structure on the product $M\times\mathbb{R}$. We show that Hitchin's approach can also be used to construct nearly parallel…

We consider holographic RG flow solutions with eight supersymmetries and study the geometry transverse to the brane. For both M2-branes and for D3-branes in F-theory this leads to an eight-manifold with only a four-form flux. In both…

Half-flat SU(3)-structures are the natural initial values for Hitchin's evolution equations whose solutions define parallel G_2-structures. Together with the results of arXiv:0912.3486v1, the results of this article completely solve the…

The holonomy group $G$ of a pseudo-quaternionic-K\"ahlerian manifold of signature $(4r,4s)$ with non-zero scalar curvature is contained in $\Sp(1)\cdot\Sp(r,s)$ and it contains $\Sp(1)$. It is proved that either $G$ is irreducible, or $s=r$…

We consider the construction of a topological version of F-theory on a particular $Spin(7)$ 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions…

We study M-theory on a Calabi-Yau fourfold with a smooth surface $S$ of $A_{N-1}$ singularities. The resulting three-dimensional theory has a $\mathcal{N}=2$ $SU(N)$ gauge theory sector, which we obtain from a twisted dimensional reduction…