arXiv research

New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.

Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.

Classifies 1-connected Lorentzian manifolds with essential conformal groups.

We study pseudo-Riemanniasn manifolds $(M,g)$ with transitive group of conformal transformation which is essential, i.e. does not preserves any metric conformal to $g$. All such manifolds of Lorentz signature with non exact isotropy representation of the stability subalgebra are described. A construction of essential c…

Classifies conformal transformations in spacetimes without observer horizons.

Study of Lorentzian manifolds with specific transformations.

We construct the first known examples of compact pseudo-Riemannian manifolds having an essential group of conformal transformations, and which are not conformally flat. Our examples cover all types $(p,q)$, with $2 \leq p \leq q$.

The multiplier spectral curve of a conformal torus in the 4-sphere is essentially, see arXiv:0712.2311, given by all Darboux transforms of the conformal torus. In the particular case when the conformal immersion is a Hamiltonian stationary torus in Euclidean 4-space, the left normal of the immersion is harmonic, hence …

The aim of this paper is to classify the cohomogeneity one conformal actions on the three-dimensional essential Riemannian spaces, up to orbit equivalence. Among other results, the representations of all connected Lie groups acting with cohomogeneity one or zero within the full conformal group of a given three-dimensio…

For a conformal vector field $ξ$ on a Riemannian manifold, we say that a point is essential if there is no local metric in the conformal class for which $ξ$ is Killing. We show that the only essential points are isolated zeros of $ξ$. As an application, we show that every connected component of the zero set of $ξ$ is t…

Compact complex manifolds with specific group actions are conformally flat.

The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least $3$ admitting a conformal essential (i.e. conformal, but not isometric) action of a Lie group locally isomorphic to PSL(2,R). It is established by using a general result of M. Gromov on local isometr…

For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conform…

Improved text classification performance through conformal transformations of kernels.

Improved multivariate conformal prediction by standardizing residuals.

Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the g…

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined…

A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.

Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.

This research examines anisotropic conformal transformations of pseudo-Finsler surfaces.

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new ev…

ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

Classification of Finslerian spaces with nontrivial concircular transformations.

In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset $Ω$ of a Riemannian manifold $L$, into another Riemannian manifold $N$ of the same dimension. In dimension $n \geq 3$, and when the $(n-1)$-dimensional Hausdorff measure of $\partial Ω$ is zero, we …

Null-Calibrated Conformal Selection via Target-Membership Scores

Synthetic approach to conformal transformations in metric and Lorentzian spaces.

Proves rigidity of certain transformations on specific geometric manifolds.

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…

The connected components of the zero set of any conformal vector field $v$, in a pseudo-Riemannian manifold $(M,g)$ of arbitrary signature, are of two types, which may be called `essential' and `nonessential'. The former consist of points at which $v$ is essential, that is, cannot be turned into a Killing field by a lo…

While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonlinear Lorentz-conformal mappings. Squares are transformed into curvili…

ConfFlow uses transformer networks to generate molecular conformations efficiently.

Semisimple Lie groups act transitively on pseudo-Riemannian manifolds, making them flat.

The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the know…

Study explores solvable Lie groups' actions on closed Lorentzian manifolds.

One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According to the Liouville Theorem, an important part of the conformal transformation is t…

We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete Riemannian manifolds of constant negative scalar curvature are isometries. We als…

The study classifies conformal biharmonic and k-polyharmonic maps between space forms.

Compact 3D Cotton-parallel manifolds are always conformally flat.

Kahler geometry explains decoupling of Kerr perturbations.

We use the general theory developed in our article arXiv:1208.5510 in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.

Local supertwistors help study 6D conformal supergravity.

We study some aspects of conformal transformations in the context of twistor theory, leading to the definition of a frustrated conformal transformation. This equation relies on two instantons for the left and right copies of $Sp(1)$, one being self-dual and the other anti-self-dual. Solutions to this equation naturally…

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a Finsler manifold. We characterize a concircular vector field with some PDEs on t…

The paper studies anisotropic conformal changes in pseudo-Finsler surfaces.

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

Study of pseudo-Riemannian manifolds with M{ö}bius group actions.

New proof confirms noncompact locally conformally flat manifolds are compact.