相关论文: Conformal structures with explicit ambient metrics…

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons…

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by…

A homemorphism between domains in $\mathbb R^n$, $n\ge 2$ is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purely metric quantity -- is uniformly bounded. Gehring proved…

This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$ relative to an arbitrary pseudo-Riemannian metric. Several results about their geometric properties are detailed, e.g.…

We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not necessarily a submanifold) and mild assumptions on the…

We review results about $G_2$-structures in relation to the existence of special metrics, such as Einstein metrics and Ricci solitons, and the evolution under the Laplacian flow on non-compact homogeneous spaces. We also discuss some…

In this paper we are investigated the monodromy group for linearly polymorphic functions on compact Riemann surface of genus $g \geq 2,$ in connection with standard uniformization of these surfaces by Kleinian groups, and are found a…

If the conformal holonomy group $Hol(\mathcal{T})$ of a simply connected space with conformal structure of signature $(2p-1,2q-1)$ is reduced to $\U(p,q)$ then the conformal holonomy is already contained in the special unitary group…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

We establish, via geometric quantization of the supercotangent bundle sM of (M,g), a correspondence between its conformal geometry and those of the spinor bundle. In particular, the Kosmann Lie derivative of spinors is obtained by…

The (Fefferman-Graham) ambient obstruction tensor is a conformally invariant symmetric trace-free 2-tensor on even-dimensional Riemannian and pseudo-Riemannian manifolds. The conformal deformation complex is a differential complex related…

We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…

This note constructs a compact, real-analytic, riemannian 4-manifold ({\Sigma}, g) with the properties that: (1) its geodesic flow is completely integrable with smooth but not real-analytic integrals; (2) {\Sigma} is diffeomorphic to $T^2…

We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential F. In particular, we show that this algorithm…

The space $\mathbf{H}^{4,2}$ of vectors of norm -1 in $\mathbb{R}^{4,3}$ has a natural pseudo-Riemannian metric and a compatible almost complex structure. The group of automorphisms of both of these structures is the split real form $G_2'$.…

We construct explicit cohomogeneity two metrics of G_2 holonomy, which are foliated by twistor spaces. The twistor spaces are S^2 bundles over four-dimensional Bianchi IX Einstein metrics with self-dual (or anti-self-dual) Weyl tensor.…

We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…

We study sequences of conformal deformations of a smooth closed Riemannian manifold of dimension $n$, assuming uniform volume bounds and $L^{n/2}$ bounds on their scalar curvatures. Singularities may appear in the limit. Nevertheless, we…

We define a measure of spectral asymmetry for G_2 and Spin(7) manifolds. We show that this invariant can be computed in terms of characteristic classes and the covariant constant form defining the G_2 or Spin(7) structure.