Related papers: Conformal geometry and 3-plane fields on 6-manifol…
The emergence of non-configurational symmetry is studied in a minimal example. The system under scrutiny consists of a dimeric hexagonal complex with configurational $C_3$ symmetry, formulated as a tight-binding model. An accidental…
In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or $(2,3,5)$-distributions determined by a…
For a conformal theory it is natural to seek the conformal moduli space, M_c to which it belongs, generated by the exactly marginal deformations. By now we should have the tools to determine M_c in the presence of enough supersymmetry. Here…
Given a parabolic geometry on a smooth manifold $M$, we study a natural affine bundle $A \to M$, whose smooth sections can be identified with Weyl structures for the geometry. We show that the initial parabolic geometry defines a reductive…
We discuss the analogy between collapsing Conformal Field Theories and measured Gromov-Hausdorff limit of Riemannian manifolds with non-negative Ricci curvature. Motivated by this analogy we propose the notion of non-commutative…
We demonstrate that all perturbative scale invariant heterotic sigma models with a compact target space $M^D$ are conformally invariant. The proof, presented in detail for up to and including two loops, utilises a geometric analogue of the…
We consider a conformally invariant version of the Calder\'on problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main…
Six dimensional supergravities on $ADS_3 \times S^3$ present interest due to the role they play in the $AdS/CFT$ correspondence. The correspondence in this case states the equivalence between supergravity on the given background and a still…
The concept of a C-class of differential equations goes back to E. Cartan with the upshot that generic equations in a C-class can be solved without integration. While Cartan's definition was in terms of differential invariants being first…
Conformal geometry is studied using the unfolded formulation \`a la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
Equivalences between conformal foliations on Euclidean $3$-space, Hermitian structures on Euclidean $4$-space, shear-free ray congruences on Minkowski $4$-space, and holomorphic foliations on complex $4$-space are explained geometrically…
We study conformal mappings in the Grushin plane and provide a number of their characterizations in terms of the Sobolev mappings and their geometry. Furthermore, we connect conformality on the Grushin plane with conformality on the complex…
Working in the framework of nilpotent geometry, we give a unified scheme for the equivalence problem of geometric structures which extends and integrates the earlier works by Cartan, Singer-Sternberg, Tanaka, and Morimoto. By giving a new…
It was shown in \cite{FPV} that the classification of $n$-component systems of conservation laws possessing a third-order Hamiltonian structure reduces to the following algebraic problem: classify $n$-planes $H$ in $\wedge^2(V_{n+2})$ such…
We reduce to various absolute parallelisms, namely to certain {e}-structures on manifolds of dimensions 7, 6, 5, the biholomorphic equivalence problem or the intrinsic CR equivalence problem for generic submanifolds M^5 in C^4 of CR…
The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to $(M,L)$ and the corresponding…
We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general…
In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg…
For a semisimple Lie group $G$ with parabolic subgroups $Q\subset P\subset G$, we associate to a parabolic geometry of type $(G,P)$ on a smooth manifold $N$ the correspondence space $\Cal CN$, which is the total space of a fiber bundle over…