Related papers: Remarks on the Schwarzian Derivatives and the Inva…
We investigate invariants of compact hyperk{\"a}hler manifolds introduced by Rozansky and Witten: they associate an invariant to each graph homology class. It is obtained by using the graph to perform contractions on a power of the…
The well known conformal covariance of the Dirac operator acting on spinor fields over a semi Riemannian spin manifold does not extend to powers thereof in general. For odd powers one has to add lower order curvature correction terms in…
In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…
In this work, we promote the global $SL(2,\mathbb{R})$ symmetry of the Schwarzian derivative to a local gauge symmetry. To achieve this, we develop a procedure that potentially can be generalized beyond the $SL(2,\mathbb{R})$ case: We first…
The main goal of this article is to construct some geometric invariants for the topology of the set $\mathcal{F}$ of flat connections on a principal $G$-bundle $P\,\longrightarrow\, M$. Although the characteristic classes of principal…
In this paper we study a multiplier operator which is induced by the Schwarzian derivative of univalent functions with a quasiconformal extension to the extended complex plane. As applications, we show that the Brennan conjecture is…
The formality morphism $\boldsymbol{\mathcal{F}}=\{\mathcal{F}_n$, $n\geqslant1\}$ in Kontsevich's deformation quantization is a collection of maps from tensor powers of the differential graded Lie algebra (dgLa) of multivector fields to…
The flag curvature of the Numata Finsler structures is shown to admit a nontrivial prolongation to the one-dimensional case, revealing an unexpected link with the Schwarzian derivative of the diffeomorphisms associated with these Finsler…
We introduce an invariant for trivalent fatgraph spines of a once bordered surface, which takes values in the first homology of the surface. This invariant is the secondary object coming from two 1-cocycles on the dual fatgraph complex, one…
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the…
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on…
We introduce higher order variants of the Yang-Mills functional that involve $(n-2)$th order derivatives of the curvature. We prove coercivity and smoothness of critical points in Uhlenbeck gauge in dimensions $\mathrm{dim}M\le 2n$. These…
A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a…
We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the…
Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz…
We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein manifold. We also construct invariants…
Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald…
In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, termed \emph{$F$-natural metrics}. These metrics parallel the well-established $g$-natural metrics on the tangent bundles of Riemannian…
Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…
Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a…