Related papers: About complex structures in conformal tractor calc…

This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize…

We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…

We introduce a new method for expanding an abelian category and study it using recollements. In particular, we give a criterion for the existence of cotilting objects. We show, using techniques from noncommutative algebraic geometry, that…

Hollow-section columns are one of the mechanically superior structures with high buckling resistance and high bending stiffness. The mechanical properties of the column are strongly influenced by the cross-sectional shape. Therefore, when…

We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…

This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…

We generalize our recent method for constructing Killing tensors of the second rank to conformal Killing tensors. The method is intended for foliated spacetimes of arbitrary dimension $m$, which have a set of conformal Killing vectors. It…

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and…

The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.

We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat…

We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

We discuss hamiltonian structures of the Gelfand-Dorfman complex of projectable vector fields and differential forms on a foliated manifold. Such a structure defines a Poisson structure on the algebra of foliated functions, and embeds the…

This paper deals with complex structures on Lie algebras $\ct_{\pi} \hh=\hh \ltimes_{\pi} V$, where $\pi$ is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on $\ct_{\pi}…

We study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. We solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to…

A projective structure on a compact Riemann surface X of genus g is given by an atlas with transition functions in PGL(2,C). Equivalently, a projective structure is given by a projective sl(2,C)-bundle over X equipped with a section s and a…

Given a generic 2-plane field on a 5-dimensional manifold we consider its (3,2)-signature conformal metric [g] as defined in math.DG/0406400. Every conformal class [g] obtained in this way has very special conformal holonomy: it must be…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

This article contributes to the relative BGG-machinery for parabolic geometries. Starting from a relative tractor bundle, this machinery constructs a sequence of differential operators that are naturally associated to the geometry in…