Four-dimensional Einstein metrics from biconformal deformations

Paul Baird; Jade Ventura

Displaying similar documents to “Four-dimensional Einstein metrics from biconformal deformations”

Lower quantization coefficient and the F-conformal measure

Mrinal Kanti Roychowdhury (2011)

Colloquium Mathematicae

Similarity:

Let $F = f^{(i)} : 1 \leq i \leq N$ be a family of Hölder continuous functions and let $φ_{i} : 1 \leq i \leq N$ be a conformal iterated function system. Lindsay and Mauldin’s paper [Nonlinearity 15 (2002)] left an open question whether the lower quantization coefficient for the F-conformal measure on a conformal iterated funcion system satisfying the open set condition is positive. This question was positively answered by Zhu. The goal of this paper is to present a different proof of this result.

Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds

Tamalika Dutta, Nirabhra Basu, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $α$ -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton is $η$ -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian...

Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

Farah H. Al-Hussaini, Aligadzhi R. Rustanov, Habeeb M. Abood (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $η$ -Einstein manifolds of type $(α, β)$ . Furthermore, we have...

Separation properties for self-conformal sets

Yuan-Ling Ye (2002)

Studia Mathematica

Similarity:

For a one-to-one self-conformal contractive system ${w_{j}}_{j = 1}^{m}$ on $ℝ^{d}$ with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to $0 < ℋ^{α} (K) < \infty$ . We give a simple proof of this result as well as discuss some further properties related to the separation condition.

On the conformal gauge of a compact metric space

Matias Carrasco Piaggio (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

In this article we study the Ahlfors regular conformal gauge of a compact metric space $(X, d)$ , and its conformal dimension ${dim}_{A R} (X, d)$ . Using a sequence of finite coverings of $(X, d)$ , we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gauge. We show how to compute ${dim}_{A R} (X, d)$ using the critical exponent $Q_{N}$ associated to the combinatorial modulus.

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

Similarity:

The notion of the Hausdorffized leaf space $\tilde{}$ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to $\tilde{}$ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to $\tilde{}$ is shown. Finally, some examples are examined.

Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability

Marco L. A. Velásquez, André F. A. Ramalho, Henrique F. de Lima, Márcio S. Santos, Arlandson M. S. Oliveira (2021)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold ${\bar{M}}_{f}^{n + 1}$ endowed with a weight function $f$ and having a closed conformal Killing vector field $V$ with conformal factor $ψ_{V}$ , that is, graphs constructed through the flow generated by $V$ and which are defined over an integral leaf of the foliation $V^{⊥}$ orthogonal to $V$ . For such graphs, we establish some rigidity results under appropriate constraints on the $f$ -mean curvature. Afterwards, we obtain some stability...

Nonexistence of entire positive solution for a conformal $k$ -Hessian inequality

Feida Jiang, Saihua Cui, Gang Li (2020)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we study the nonexistence of entire positive solution for a conformal $k$ -Hessian inequality in $ℝ^{n}$ via the method of proof by contradiction.

A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$ -curvature

Matthew J. Gursky, Andrea Malchiodi (2015)

Journal of the European Mathematical Society

Similarity:

In this paper we consider Riemannian manifolds $(M^{n}, g)$ of dimension $n \geq 5$ , with semi-positive $Q$ -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive $Q$ -curvature. Modifying the test function construction of Esposito-Robert,...

Conformal measures and matings between Kleinian groups and quadratic polynomials

Marianne Freiberger (2007)

Fundamenta Mathematicae

Similarity:

Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ is equal to the Hausdorff dimension of the limit set. Moreover, when f is the limit of a pinching deformation ${f_{t}}_{0 \leq t < 1}$ we give sufficient conditions for the dynamical convergence of $f_{t}$ .

Semilinear equations, the $γ_{k}$ function, and generalized Gauduchon metrics

Jixiang Fu, Zhizhang Wang, Damin Wu (2013)

Journal of the European Mathematical Society

Similarity:

In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $γ_{k}$ functions on the space of its hermitian metrics.

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

Similarity:

It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_{G}$ . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^{r}$ diffeomorphism group G is simple iff the foliation $ℱ_{[G, G]}$ defined by [G,G] admits no proper...

Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

Similarity:

It is proved that the normal bundle $ℋ$ of a distribution $𝒱$ on a riemannian manifold admits a conformal curvature $C$ if and only if $𝒱$ is a conformal foliation. Then $ℋ$ is conformally flat if and only if $C$ vanishes. Also, the Pontrjagin classes of $ℋ$ can be expressed in terms of $C$ .

Asymptotically conformal classes and non-Strebel points

Guowu Yao (2016)

Studia Mathematica

Similarity:

Let T(Δ) be the universal Teichmüller space on the unit disk Δ and T₀(Δ) be the set of asymptotically conformal classes in T(Δ). Suppose that μ is a Beltrami differential on Δ with [μ] ∈ T₀(Δ). It is an interesting question whether [tμ] belongs to T₀(Δ) for general t ≠ 0, 1. In this paper, it is shown that there exists a Beltrami differential μ ∈ [0] such that [tμ] is a non-trivial non-Strebel point for any $t \in (- 1 / | | μ | |_{\infty}, 1 / | | μ | |_{\infty}) ∖ 0, 1$ .

Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier

Similarity:

We show that any transversally complete Riemannian foliation $ℱ$ of dimension one on any possibly non-compact manifold $M$ is tense; namely, $M$ admits a Riemannian metric such that the mean curvature form of $ℱ$ is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize...

A Monge-Ampère equation in conformal geometry

Matthew J. Gursky (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We consider the Monge-Ampère-type equation $det (A + λ g) = const .$ , where $A$ is the Schouten tensor of a conformally related metric and $λ > 0$ is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique. ...

Foliations by complex manifolds involving the complex Hessian

Julian Ławrynowicz, Jerzy Kalina, Masami Okada

Similarity:

SummaryIn 1979 the second named author proved, in a joint paper with J. Ławrynowicz, the existence of a foliation of a bounded domain in $ℂ^{n}$ by complex submanifolds of codimension k+p-1, connected in some sense with a real (1,1) C³-form of rank k and the pth power of the complex Hessian of a C³-function u with im u plurisubharmonic and the property that for every leaf of this foliation the restricted functions im u, re u and $(\partial / \partial z_{j}) i m u$ , $(\partial / \partial z_{j}) r e u$ are pluriharmonic and holomorphic, respectively.Now the...

Minimal, rigid foliations by curves on $ℂ ℙ^{n}$

Frank Loray, Julio C. Rebelo (2003)

Journal of the European Mathematical Society

Similarity:

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space $ℂ ℙ^{n}$ for every dimension $n \geq 2$ and every degree $d \geq 2$ . Precisely, we construct a foliation $ℱ$ which is induced by a homogeneous vector field of degree $d$ , has a finite singular set and all the regular leaves are dense in the whole of $ℂ ℙ^{n}$ . Moreover, $ℱ$ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if $ℱ$ is conjugate to another holomorphic...

Groups of $C^{r, s}$ -diffeomorphisms related to a foliation

Jacek Lech, Tomasz Rybicki (2007)

Banach Center Publications

Similarity:

The notion of a $C^{r, s}$ -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of $C^{r, s}$ -diffeomorphisms is proved. A remark on $C^{n + 1}$ -diffeomorphisms is given.

On a class of quasi-conformal mappings with invariant boundary points, I. The class $E_{Q}$ and and the general extremal problem

J. Ławrynowicz (1969)

Annales Polonici Mathematici

Similarity:

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

Similarity:

For odd-dimensional Poincaré–Einstein manifolds $(X^{n + 1}, g)$ , we study the set of harmonic $k$ -forms (for $k < n / 2$ ) which are $C^{m}$ (with $m \in ℕ$ ) on the conformal compactification $\bar{X}$ of $X$ . This set is infinite-dimensional for small $m$ but it becomes finite-dimensional if $m$ is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology $H^{k} (\bar{X}, \partial \bar{X})$ and the kernel of the Branson–Gover [3] differential operators $(L_{k}, G_{k})$ on the conformal infinity $(\partial \bar{X}, [h_{0}])$ . We also relate the set of $C^{n - 2 k + 1} (Λ^{k} (\bar{X}))$ forms in the kernel of $d + δ_{g}$ ...