Integrability of quaternion-Kähler symmetric spaces

2020/08/12 by Hase, Anton
#Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2008.05376

Abstract

We find a necessary condition for the existence of an action of a Lie group G by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of \mathfrakg. We check this condition and prove that a Riemannian symmetric space of dimension 4n for n≥ 2 has an invariant integrable almost quaternionic structure if and only if it is quaternionic vector space, quaternionic hyperbolic space or quaternionic projective space.

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