Related papers: Conformal flat AK2-manifolds

In this paper, we generalize Huber's finite point conformal compactification theorem to a higher dimensional manifold, which is conformally compact with $L^\frac{n}{2}$ integrable Ricci curvatures.

In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 1.4 have the additional properties of being sharp.

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some…

We prove a flat strip theorem for 2-dimensional ptolemaic spaces.

A simple model for the localization of the category $\mathbf{CLoc}_2$ of oriented and time-oriented globally hyperbolic conformal Lorentzian $2$-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of…

We present a characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature. It is well known that every $2$-dimensional Lorentzian manifolds is conformally flat, so we rewrite the Ricci scalar curvature in…

We prove that any conformally flat submanifold with flat normal bundle in a conformally flat Riemannian manifold is locally holonomic, that is, admits a principal coordinate system. As one of the consequences of this fact, it is shown that…

We prove that compact non-flat manifolds with constant sectional curvature admit no conformal product structure. Furthermore, we demonstrate that the methods extend naturally to irreducible, compact locally symmetric spaces of non-positive…

Around 2007, A. Chang, J. Qing, and P. Yang proved a conformal gap theorem for Bach-flat metrics with round sphere as the model case. In this article, we extend this result to prove conformally invariant gap theorems for Bach-flat…

In this paper, we want to prove positive mass theorems for ALF and ALG manifolds with model spaces $\mathbb R^{n-1}\times \mathbb S^1$ and $\mathbb R^{n-2}\times \mathbb T^2$ respectively in dimensions no greater than $7$ (Theorem…

We classify conformally flat Riemannian $3-$manifolds which possesses a free isometric $S^1-$action.

We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group.

In this paper, we prove conformal positive mass theorems for asymptotically flat manifolds with charge. We apply conformal relations to show that if the conformal sum of scalar curvature is not less than the norm square of electric field…

In this paper we prove that a regular foliation on a complex weak Fano manifold is algebraically integrable.

We survey recent developments which led to the proof of the Benson-Gordon conjecture on K\"ahler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a K\"ahler manifold which is a homotopy torus is a…

We prove finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application we construct a flat family of irreducible normal projective varieties over the moduli stack of stable pointed…

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

We provide a reduction in the classification problem for non-compact, homogeneous, Einstein manifolds. Using this work, we verify the (Generalized) Alekseevskii Conjecture for a large class of homogeneous spaces.