Definite signature conformal holonomy: a complete classification
Abstract
This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones, whose Riemmanian holonomy is the same as the Tractor holonomy of the underlying manifold. Direct calculations in the Ricciflat case and an important decomposition theorem complete the classification for definitive signature.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2005
 DOI:
 10.48550/arXiv.math/0503388
 arXiv:
 arXiv:math/0503388
 Bibcode:
 2005math......3388A
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Metric Geometry;
 53B15
 EPrint:
 31 Pages, sections and introduction to Cartan connection reworked and typos corrected