Related papers: Transitive conformal holonomy groups

In this note we study topological invariants of the spaces of homomorphisms Hom(\pi,G), where \pi\ is a finitely generated abelian group and G is a compact Lie group arising as an arbitrary finite product of the classical groups SU(r), U(q)…

Let $M$ be a connected smooth manifold, let $\operatorname{Aut}(p)$ be the group automorphisms of the bundle $p\colon \mathbb{R}\times M\to \mathbb{R}$, and let $q\colon J^1(\mathbb{R},M)\times \mathbb{R\to }J^1(\mathbb{R},M)$ be the…

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli stack parametrizing Deligne-Mumford stable $n$-pointed genus $g$ curves and let $\overline{M}_{g,n}$ be its coarse moduli space: the Deligne-Mumford compactification of the moduli space of…

Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic…

Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that the action is \emph{fixed point homogeneous} if $G$ acts transitively on a normal…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…

We study simple space-time symmetry groups G which act on a space-time manifold M=G/H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory: 1)…

Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are compactly supported isotopic to the identity. This group acts $n$-transitive: Any tuple of $n$ points can be moved to any…

The Einstein universe $\mathbf{Ein}^{p,q}$ of signature $(p,q)$ is a pseudo-Riemannian analogue of the conformal sphere; it is the conformal compactification of the pseudo-Riemannian Minkowski space. For $p,q \geq 1$, we show that, up to a…

Let $g$ be a hyper-Hermitian metric on a simply connected hypercomplex four-manifold $M$. We show that when the isometry group $I(M,g)$ contains a subgroup acting simply transitively on $M$ by hypercomplex isometries then the metric $g$ is…

This article investigates the holonomy groups of K-contact sub-pseudo-Riemannian manifolds. The primary result is a proof that the horizontal holonomy group either coincides with the adapted holonomy group or acts as its normal subgroup of…

Using the L^2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p,q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p,q). A key step is…

We show that an isometric action of a compact quantum group on the underlying geodesic metric space of a compact connected Riemannian manifold $(M,g)$ with strictly negative curvature is automatically classical, in the sense that it factors…

In this paper, we study some characterizations of $q$-spaces, strict $q$-spaces and strong $q$-spaces under $\omega$-balanced topological groups as follows: (1) A topological group $G$ is $\omega$-balanced and a $q$-space if and only if for…

Let $M$ be a compact hyperkahler manifold with maximal holonomy (IHS). The group $H^2(M, R)$ is equipped with a quadratic form of signature $(3, b_2-3)$, called Bogomolov-Beauville-Fujiki (BBF) form. This form restricted to the rational…

We introduce a new notion of a homogeneous pair for a pseudo-Riemannian metric $g$ and a positive function $f$ on a manifold $M$ admitting a free $\mathbb{R}_{>0}$-action. There are many examples admitting this structure. For example, (a) a…

If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the…

A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie group structure and $c$ is the conformal structure defined by a left-invariant metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie…

We show that holomorphic riemannian metrics on compact complex threefolds are locally homogeneous (the pseudogroup of local isometries acts transitively on the manifold).