Related papers: Holonomy of the Obata connection on SU(3)
We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is…
Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $\Gamma…
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on…
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…
A specific new quark permits that flavor generations constitute a representation of the 3-dimensional SU(3) symmetry that characterizes the Z(3) orbifold. In this context, color and supergravity bind triplets and 4-tuplets into composite…
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…
Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the…
Bryant \cite{Br} proved the existence of torsion free connections with exotic holonomy, i.e. with holonomy that does not occur on the classical list of Berger \cite{Ber}. These connections occur on moduli spaces $\Y$ of rational contact…
The timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. We show that the generalized holonomy group for vacua…
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…
In this PhD Thesis, supersymmetry and its formulation in the context of D=11 supergravity is discussed from several perspectives. The role of generalized holonomy as a classification tool of supersymmetric supergravity solutions is…
We investigate the existence and geometric properties of special hyperhermitian metrics. First of all, we characterise hypercomplex structures with Obata holonomy in $\mathrm{SL}(n, \mathbb{H})$ in terms of the existence of quaternionic…
We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of…
We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is the fundamental group of the orbifold S^2(2,...,2) and thus contains a surface group…
In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This…
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…
This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface $\Sigma$ (of genus 2) thus solving a long standing problem in complex hyperbolic…
It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional submanifold of a closed orientable 3-manifold can be realised…
In this paper, we prove that the (orientation-preserving) symmetry groups of $b$-prime flat fully augmented links correspond exactly with the finite subgroups of $O(3)$. We accomplish this by first developing a dictionary between…
Let $\mathcal{G}^*(S,\rho)$ be the graph whose vertices are marked complex projective structures with holonomy $\rho$ and whose edges are graftings from one vertex to another. If $\rho$ is quasi-Fuchsian, a theorem of Goldman implies that…