Homogeneous almost quaternion-Hermitian manifolds

Abstract

An almost quaternion-Hermitian structure on a Riemannian manifold $(M^{4n},g)$ is a reduction of the structure group of $M$ to $\mathrm{Sp}(n)\mathrm{Sp}(1)\subset \mathrm{SO}(4n)$. In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or ${\mathbb{S}}^2\times {\mathbb{S}}^2$, or the complex quadric $\mathrm{SO}(7)/\mathrm{U}(3)$.

published version, references updated

References in corpus (5)

• Clifford structures on Riemannian manifolds
• Higher rank homogeneous Clifford structures
• A Nearly Quaternionic Structure on SU(3)
• Invariant four-forms and symmetric pairs
• Weakly complex homogeneous spaces

Cited by in corpus (1)

• Twisted holomorphic symplectic forms