arXiv research

Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.

Schrödinger bridge solved with Weyl calculus for quadratic state cost.

Estimates for spacelike hypersurfaces in de Sitter space.

Revisits Weyl's problem on isometric immersions of spheres into 3D manifolds.

We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincaré metrics, this leads to a natural extension of the notion of Branson's $Q$-curvature to Weyl structures on even-dimension…

On four-dimensional closed manifolds we introduce a class of canonical Riemannian metrics, that we call weak harmonic Weyl metrics, defined as critical points in the conformal class of a quadratic functional involving the norm of the divergence of the Weyl tensor. This class includes Einstein and, more in general, harm…

Paper finds non-positive Weyl connections on Lie groups, confirming a conjecture.

We consider a priori estimates of Weyl's embedding problem of $(\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of $(\mathbb{S}^2,g)$ in…

Paper presents an action principle for Einstein-Weyl equations in 3D.

In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.

Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.

Solutions grow for a special type of math problem on curved spaces.

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy" condition on the Weyl tensor \W. We investigate the geometry of the foliations …

Weyl and Cartan proposed different but related ways to handle infinitesimal geometry in the early 1920s.

Holonomy of Weyl connections in Lorentzian space classified.

We show that a properly convex projective structure $\mathfrak{p}$ on a closed oriented surface of negative Euler characteristic arises from a Weyl connection if and only if $\mathfrak{p}$ is hyperbolic. We phrase the problem as a non-linear PDE for a Beltrami differential by using that $\mathfrak{p}$ admits a compatib…

In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(κ,μ)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $α$-cosymplectic manifol…

This thesis explores Weyl geometry and quantum anomalies in holography and gauge theories.

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the a…

In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection $(M^4,c,D)$. We show that there is an Eells-Salamon type correspondence between nonvertical $\mathcal{J}$-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces.…

Researchers prove unique embedding of curved surfaces into Minkowski spacetime.

We determine the space of algebraic pseudo-Hermitian Kähler-Weyl curvature tensors and the space of para-Hermitian Kähler-Weyl curvature tensors in dimension 4 and show that every algebraic possibility is geometrically realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds and for para-Hermitian…

The abstract discusses transformations on statistical and semi-Weyl manifolds with torsion.

Study pseudo-harmonic maps on Weyl manifolds.

We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlevé transcendents. The first construction is a hodograph transformation based on Einstein--Weyl geometry, the generalised Nahm's equation and the isomonodromy problem. The second construction, motivated…

A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homogeneous space $M_0$, if its Weyl tensor at every point is "the same" as the Weyl tensor of $M_0$, up to a positive multiple. We prove that a …

This is a survey on quaternion Hermitian Weyl (locally conformally quaternion Kähler) and hyperhermitian Weyl (locally conformally hyperkähler) manifolds. These geometries appear by requesting the compatibility of some quaternion Hermitian or hyperhermitian structure with a Weyl structure. The motivation for such a stu…

We show that the Weyl structure of an almost-Hermitian Weyl manifold of dimension at least 6 is trivial if the associated curvature operator satisfies the Kaehler identity. Similarly if the curvature of an almost para-Hermitian Weyl manifold of dimension at least 6 satisfies the para-Kaehler identity, then the Weyl str…

The Weyl problem is extended to hyperbolic and anti-de Sitter spaces, connecting geometry, analysis, and group theory.

New manifold structures on Weyl group orbit spaces proven.

We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachhöfer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where the Weyl connection $D$ is reducible and non-closed. In this case, it was shown b…

Study complete gradient Ricci solitons with zero radial Weyl curvature.

Study pinched self-dual Weyl curvature in compact 4-manifolds.

We show any Weyl curvature model can be geometrically realized by a Weyl manifold

We work in both the complex and in the para-complex categories and examine (para)-Kähler Weyl structures in both the geometric and in the algebraic settings. The higher dimensional setting is quite restrictive. We show that any (para)-Kaehler Weyl algebraic curvature tensor is in fact Riemannian in dimension at least 6…

Small Weyl infimum on 4-manifolds with positive scalar curvature.

Develops Poisson and Dirac manifolds of compact types with applications.

Computes Weyl group of Kähler toric manifold isometries.

Constructs generalized Frobenius manifolds for specific Weyl groups.

Study pinches Weyl curvature on 4-manifolds, proving anti-self-duality.

We study Weyl structures on lightlikes hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambiant Lorentzi…

Study on Berwald-Weyl curvature with projective invariance and vanishing results.

Proves stability in Weyl polytopes using optimal transport.

Assume that $M$ is a smooth manifold with a symplectic structure $ω$. Then Weyl manifolds on the symplectic manifold $M$ are Weyl algebra bundles endowed with suitable transition functions. From the geometrical point of view, Weyl manifolds can be regarded as geometrizations of star products attached to $(M,ω)$. In the…

In this paper, we introduce the notions of ALF Weyl connection and of associated mass, and we prouve the positive mass theorem for the ALF Weyl structures.

Study Toda systems blowup masses linked to Weyl groups.

The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

We consider a connected compact Lie group K acting on a symplectic manifold M such that a moment map m exists. A pull-back function via m Poisson commutes with all K-invariants. Guillemin-Sternberg raised the problem to find a converse. In this paper, we solve this problem by determining the Poisson commutant of the al…