Normal Conformal Killing Forms

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 solut...

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Bibliographic Details
Published in:arXiv.org 2004-06
Main Author: Leitner, Felipe
Format: Article
Language:English
Subjects:
Differential equations
Mathematical analysis
Representations
Online Access:Get full text
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Summary: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.
ISSN:2331-8422