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Definite signature conformal holonomy: a complete classification. (English) Zbl 1407.53050

Summary: 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 Riemannian 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.

MSC:

53C29 Issues of holonomy in differential geometry
53A30 Conformal differential geometry (MSC2010)
53B15 Other connections
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References:

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