Related papers: Closed G2-structures with conformally flat metric

The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective…

We investigate 7 dimensional almost para-contact metric structures induced by the 3-forms of $G_2^*$ Structures. We calculate the projections that determine to which class the almost para-contact structure belongs, by using the properties…

In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the…

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly K\"ahler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is…

Inspired by considerations in $M$-theory, we prove the equivalence between the moduli spaces of (suitably complexified) torsion free $G_{2}$-structures on 7-manifolds which are families of hyperK\"ahler ALE 4-manifolds fibered over compact…

In this paper, we bend a closed Riemannian manifold in the conformal class, through solving a fully nonlinear equation. As a result, we prove that each metric of quasi-negative Ricci curvature is conformal to a metric with negative Ricci…

Let G be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if G is self-dual (that is, if it possesses an invariant metric) then there is a canonical N=1 superconformal algebra associated to its N=1…

Let $X$ be a ruled surface over a curve of genus $g$. We prove that $X$ has a scalar-flat Hermitian metric if and only if $g\geq 2$ and $m(X)>2-2g$ where $m(X)$ is an intrinsic number depends on the complex structure of $X$.

This article studies closed G2-structures satisfying the quadratic condition, a second-order PDE system introduced by Bryant involving a parameter $\lambda.$ For certain special values of $\lambda$ the quadratic condition is equivalent to…

In this paper, we consider half-flat $SU(3)$-structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form $w_1^-$ is constant in each of the two subclasses. We then consider the…

Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of…

Given a maximally non-integrable 2-distribution ${\mathcal D}$ on a 5-manifold $M$, it was discovered by P. Nurowski that one can naturally associate a conformal structure $[g]_{\mathcal D}$ of signature (2,3) on $M$. We show that those…

We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the…

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

Let $R\to U$ be an associative ring epimorphism such that $U$ is a flat left $R$-module. Assume that the related Gabriel topology $\mathbb G$ of right ideals in $R$ has a countable base. Then we show that the left $R$-module $U$ has…

We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…

We describe an explicit metric that induces the Chabauty topology on the space of closed subsets of a proper metric space M.

We introduce the notion of coarse metric. Every coarse metric induces a coarse structure on the underlying set. Conversely, we observe that all coarse spaces come from a particular type of coarse metric in a unique way. In the case when the…

We prove that any metric with curvature $\leq -1$ (in the sense of A. D. Alexandrov) on a closed surface of genus $>1$ is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension $(2+1)$…