Normal Conformal Killing Forms

Abstract

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of conformal geometry. Reductions of its holonomy are related to solutions of the normal twistor equations. The case of decomposable normal conformal holonomy representations is discussed. A typical example with an irreducible holonomy representation are the so-called Fefferman spaces. We also apply our results to describe the geometry of solutions with conformal Killing spinors on Lorentzian spin manifolds.

32 pages, 3 tables

References in corpus (1)

• Conformal Killing forms on Riemannian manifolds

Cited by in corpus (13)

• About Twistor Spinors with Zero in Lorentzian Geometry
• The Geometry of Almost Einstein (2,3,5) Distributions
• Conformal structures with $G_{2(2)}$-ambient metrics
• Definite signature conformal holonomy: a complete classification
• Parallel tractor extension and ambient metrics of holonomy split G_2
• Ambient connections realising conformal Tractor holonomy
• Projective Geometry II: Cones and Complete Classifications
• The geometry of conformally Einstein metrics with degenerate Weyl tensor
• Projective Geometry I: Principles and Properties
• The ambient obstruction tensor and conformal holonomy
• A class of compact Poincare-Einstein manifolds: properties and construction
• Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds
• Four dimensional conformal C-spaces