相关论文: About complex structures in conformal tractor calc…

We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from…

This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651-3671], and…

We prove that given a pseudo-Riemannian conformal structure whose conformal holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is, wrt. a local metric in the conformal class defined off a singular set,…

We characterise the integrability of any co-CR quaternionic structure in terms of the curvature and a generalized torsion of the connection. Also, we apply this result to obtain, for example, the following. (1) New co-CR quaternionic…

We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this…

We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci…

This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with…

We first show how, from the general 3rd order ODE of the form z'''=F(z,z',z'',s), one can construct a natural Lorentzian conformal metric on the four-dimensional space (z,z',z'',s). When the function F(z,z',z'',s) satisfies a special…

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie…

The correspondence between wind Riemannian structures and spacetimes endowed with a Killing vector field is deepened by considering a cone structure endowed with a vector field that preserve the structure (termed "cone Killing vector…

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…

These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so called parabolic geometries.

We define the operations of conformal change and elementary deformation in the setting of generalized complex geometry. Then we apply Swann's twist construction to generalized (almost) complex and Hermitian structures obtained by these…

The mathematics of a 4-dimensional renormalizable generally covariant lagrangian model (with first order derivatives) is reviewed. The lorentzian CR manifolds are totally real submanifolds of 4(complex)-dimensional complex manifolds…

We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…

The purpose of this note is to study the complex structures orthogonal to a given Riemannian metric. For another paper on this topic, we highly recommend the work of Salamon. His work describes in great detail the role that curvature plays…

Recently, Cardoso, Houri and Kimura constructed generalized ladder operators for massive Klein-Gordon scalar fields in space-times with conformal symmetry. Their construction requires a closed conformal Killing vector, which is also an…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…