Essential points of conformal vector fields

@article{Belgun2011EssentialPO,
  title={Essential points of conformal vector fields},
  author={F. Belgun and Andrei Moroianu and L. Ornea},
  journal={Journal of Geometry and Physics},
  year={2011},
  volume={61},
  pages={589-593}
}
An essential point of a conformal vector fieldon a conformal manifold (M,c) is a point around which the local flow ofpreserves no metric in the conformal class c. It is well-known that a conformal vector field vanishes at each essential point. In this note we show that essential points are isolated. This is a generalization to higher dimensions of the fact that the zeros of a holomorphic function are isolated. As an application, we show that every connected component of the zero set of a… Expand
On the isotropy subalgebras of Lie algebras of conformal vector fields
The conformal isotropy algebra of a point m in an n-manifold with a metric of arbitrary signature is shown to be locally reducible, by a conformal change of the metric, to a homothetic algebra near mExpand
Local dynamics of conformal vector fields
We study pseudo-Riemannian conformal vector fields in the neighborhood of a singularity. For Riemannian manifolds, we prove that if a conformal vector field vanishing at a point x0 is not Killing forExpand
Two-jets of conformal fields along their zero sets
The connected components of the zero set of any conformal vector field v, in a pseudo-Riemannian manifold (M, g) of arbitrary signature, are of two types, which may be called ‘essential’ andExpand
The zero set of a twistor spinor in any metric signature
Using tractor methods, we exhibit the local structure of the zero set of a twistor spinor in any metric signature. It is given as the image under the exponential map of a distinguished totallyExpand
NORMAL BGG SOLUTIONS AND POLYNOMIALS
First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include thoseExpand
Gravitation in flat spacetime from entanglement
We explore holographic entanglement entropy for Minkowski spacetime in three and four dimensions. Under some general assumptions on the putative holographic dual, the entanglement entropy associatedExpand

References

SHOWING 1-10 OF 15 REFERENCES
Essential conformal vector fields
A geometrical proof is provided of a necessary and sufficient condition for a conformal Killing vector field with fixed point on a pseudo-Riemannian manifold to be homothetic or Killing with respectExpand
Local dynamics of conformal vector fields
We study pseudo-Riemannian conformal vector fields in the neighborhood of a singularity. For Riemannian manifolds, we prove that if a conformal vector field vanishing at a point x0 is not Killing forExpand
GROUPS OF CONFORMAL TRANSFORMATIONS OF RIEMANNIAN SPACES
It is proved that if a Riemannian space (M, g) of class C∞ has a connected group of conformal transformations which leaves no conformally given metric eσg invariant, then (M, g) is globally conformalExpand
Formes normales pour les champs conformes pseudo-riemanniens
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field isExpand
Fixed points of isometries
The purpose of this paper is to prove the following Theorem. Let M be a Riemannian manifold of dimension n and let ξ be a Killing vector field (i.e., infinitesimal isometry) of M. Let F be the set ofExpand
Conformal transformations of pseudo-Riemannian manifolds
This is a survey about conformal mappings between pseudo-Riemannian manifolds and, in particular, conformal vector fields defined on such. Mathematics Subject Classification (2000). Primary 53C50;Expand
Essential conformal vector fields, Class
  • Quantum Grav
  • 1999
Conformal Killing Vectors Near a Fixed Point
  • Preprint of the Institut für Theoretische Physik, Vienna,
  • 1992
Conformal Killing Vectors Near a Fixed Point, Institut für Theoretische Physik
  • 1992
On conformal connections and infinitesimal conformal transformations
  • PhD Thesis,
  • 2010
...
1
2
...