Related papers: The $Spin(7)$-structures on complex line bundles a…

Asymptotically locally conical (ALC) metric of exceptional holonomy has an asymptotic circle bundle structure that accommodates the M theory circle in type IIA reduction. Taking Spin(7) metrics of cohomogeneity one as explicit examples, we…

In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop…

We construct a family of non-collapsed, non-K\"ahler, non-Einstein steady Ricci solitons in even dimensions greater or equal to four. These solitons exist on complex line bundles over K\"ahler-Einstein manifolds of positive scalar…

We study spherical quadrilaterals whose angles are odd multiples of pi/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are…

We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which are R^3 bundles over a quaternionic space. The metrics depend on five parameters and have two Abelian isometries. Certain singularities of the G_2 manifolds are…

We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special K\"ahler holonomy. Motivated by certain curvature…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…

We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a…

Any Spin(7)-manifold admits a metric connection \nabla^c with totally skew-symmetric torsion T^c preserving the underlying structure. We classify those with \nabla^c-parallel T^c\neq0 and non-Abelian isotropy algebra iso(T^c)<spin(7). These…

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a…

We reduce the embedding problem for hypo SU(2) and SU(3)-structures to the embedding problem for hypo G2-structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the…

We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over $\mathbb{CP}^2$, $\mathbb{HP}^2$ and $\mathbb{OP}^2$ with respective principal orbits $G/K$ the Wallach spaces…

In this work we construct new multi-dimensional families of compact minimal submanifolds, of the classical Riemannian symmetric spaces $SU(n)/SO(n)$, $Sp(n)/U(n)$, $SO(2n)/U(n)$ and $SU(2n)/Sp(n)$, of codimension two.

We study an energy functional on the universal spinor bundle over a closed $n$-dimensional spin manifold $M$. The critical points of this functional, which is modelled on the total torsion functional of $G_2$-structures in seven dimensions,…

In this note we generalize the methods of [1][2][3] to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional…

We explicitly construct a solution of eight-dimensional gauged supergravity representing D6-branes wrapped on six-cycles inside Calabi-Yau fourfolds. The solution preserves two supercharges and asymptotically is a cone with the coset space…

The Stenzel space fourfold is a non-compact Calabi-Yau which is a higher dimensional analogue of the deformed conifold. We consider N = (1,1) type IIA, N = 1 M-theory and N = (2,0) type IIB compactifications on this Stenzel space, thus…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss…

We present a construction of superconformal field theories for manifolds with Spin(7) holonomy. Geometrically these models correspond to the realization of Spin(7) manifolds as anti-holomorphic quotients of Calabi-Yau fourfolds. Describing…