Definite signature conformal holonomy: a complete classification

Details Definite signature conformal holonomy: a complete classification Definite signature conformal holonomy: a complete classification

2005-03-18

arxiv.org/abs/math/0503388v3

Mathematics

Differential Geometry

31 Pages, sections and introduction to Cartan connection reworked and typos corrected

Scientific paper

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 Ricci-flat case and an important decomposition theorem complete the classification for definitive signature.

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