Related papers: Derivations, holonomy groups and heterotic geometr…
We consider warp compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes and investigate the constraints imposed by supersymmetry. As long as the 7-manifold supports only one Killing spinor we infer from the Killing…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3).…
We present a uniform description of $\mathrm{SU}(3)$-structures in dimension $6$ as well as $G_2$-structures in dimension $7$ in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to…
Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,"generalized supertranslations") is provided. In each given space-time…
We consider spin manifolds with an Einstein metric, either Riemannian or indefinite, for which there exists a Killing spinor. We describe the intrinsic geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair of induced…
In this note we revisit the Lin, Lunin, Maldacena (LLM) class of d=11 supergravity solutions with symmetry SO(6) X SO(3) X R, but generalise to allow for all fluxes consistent with the isometries. Using the Killing spinor equation, we prove…
In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11…
The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of $G_2$ holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or…
We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal…
We construct the Killing superalgebra of supersymmetric backgrounds of ten-dimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras…
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…
In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their…
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…
For Kaehler manifolds we explicitly determine the solution to the conformal Killing form equation in middle degree. In particular, we complete the classification of conformal Killing forms on compact Kaehler manifolds. We give the first…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
This is a doctoral thesis on the application of techniques originally developed in the programme of characterisation of supersymmetric solutions to Supergravity theories, to finding alternative backgrounds. We start by discussing the…
For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this…