Related papers: Spin(7) metrics from K\"ahler Geometry
If a $Spin(7)$ manifold $N^8$ admits a free $S^1$ action preserving the fundamental $4$-form then the quotient space $M^7$ is naturally endowed with a $G_2$-structure. We derive equations relating the intrinsic torsion of the…
We construct new explicit metrics on complete non-compact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is topologically R^8 and another, which we denote by B_8, is the bundle of chiral spinors over…
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic…
We utilize Spin(7) identities to prove that the Cayley four-form associated to a torsion-free Spin(7)-Structure is non-degenerate in the sense of multisymplectic geometry. Therefore, Spin(7) geometry may be treated as a special case of…
We construct propose an anzatz for Spin(7) metrics as an R-bundle over closed G2 structures. These G2 structures are R3 bundles over 4-dimensional compact quaternion Kahler spaces. The inspiration for the anzatz metric comes from the…
We prove that Riemannian $Spin(7)$ holonomy manifolds carry octonionic-K\"{a}hler structure.
Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces…
We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A_8, is complete and non-singular on R^8. The other complete metrics are…
We study $\mathrm{Spin}(7)$-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons-Hawking type ansatz that describes such geometries in terms of a symmetric $4\times4$-matrix of…
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…
We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which are complete on a complex line bundle over CP^3. The principal orbits are S^7, described…
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)…
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 smooth fibrations of compact torsion-free Spin(7)-manifolds by Cayley submanifolds. Using geometric and topological constraints coming from the Spin(7)-structure, we show that only two topological configurations can arise. One of…
We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connected. For each presentation, we exhibit explicit examples of…
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…
Based on a general formula due to R.Bryant, we work out the topological structure of the space of torsion-free $G_2$-structures generating the same associated Riemannian metric on a compact $7$-manifold. We also identify a corresponding Lie…
We construct examples of asymptotically cylindrical Riemannian 8-manifolds with holonomy group Spin(7). To our knowledge, these are the first such examples. The construction uses an extension to asymptotically cylindrical setting of Joyce's…
We apply the method of linear perturbations to the case of Spin(7)-structures, showing that the only nontrivial perturbations are those determined by a rank one nilpotent matrix. We consider linear perturbations of the Bryant-Salamon metric…
Given a CMC surface in $R^3$, its traceless second fundamental form can be viewed as a holomorphic section called the Hopf differential. By analogy, we show that for an associative submanifold of a 7-manifold $M^7$ with $G_2$-structure, its…