arXiv research

Proves rigidity of certain transformations on specific geometric manifolds.

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

Classification of Finslerian spaces with nontrivial concircular transformations.

Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.

A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be lifted to a circles preserving quasiconformal mapping of the hyperbolic Heisenberg …

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 conformal transformations in spacetimes without observer horizons.

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.

Study of Lorentzian manifolds with specific transformations.

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.

Classifies 1-connected Lorentzian manifolds with essential conformal groups.

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.

Synthetic approach to conformal transformations in metric and Lorentzian spaces.

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…

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.

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…

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.

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.

New proof confirms noncompact locally conformally flat manifolds are compact.

Characterizes Kerr spacetimes using conformal methods.

Study properties of hypersurfaces in spacetimes with conformal transformations.

Study on special anisotropic conformal changes of conic pseudo-Finsler surfaces.

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $β$-conformal change: $L(x,y) \longrightarrow\overline{L}(x,y) = f(e^{σ(x)}L(x,y),β(x,y)).$ This transformation combines both $β$-change and conformal change in a general setting. T…

We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-Kähler metrics. We also give an explicit formula for the inverse transform. This paper is a generalization of "The Twistor correspondence of the Dolbeault complex over $\C^n$" (dg-ga/9501004) …

Yamabe solitons defined on specific Sasaki-like manifolds.

This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twisto…

In this paper, we study the long existence problem of non Berwaldian Landsberg spaces using the conformal transformation point of view. Under conformal transformation, the Berwald and Landesberg tensors are calculated in terms of the T-tensor. By giving examples, we show that under conformal transformation, there are L…

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms pres…

We discuss non-conformal harmonic surfaces in $R^3$ with prescribed ($\pm$)transforms, and we get a representation formula for non-conformal harmonic surfaces in $R^3$.

Infinitesimal conformal transformations of $R^n$ are always polynomial and finitely generated when $n>2$. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over $R^n$, $n>1$, is maximal in the Lie algebra of polynomial vector fields. When $n$ is greater than 2 and $p,q$ are such t…

Projective geodesic extensions for nonholonomic systems are derived under conformal transformations.

This study uses ICL to efficiently generate robust confidence intervals for noisy regression tasks.

We consider the class of all conformal mappings from a compact Riemann surface into the threedimensional or fourdimensional Euclidean space. A sequence in this class with bounded Willmore functional is shown to have a sequence of conformal transformations of the target space, such that a subsequence of the transformed …

New method improves conditional coverage of conformal prediction.

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 …

Proves constraints on groups extending Möbius transformations on spheres.