Curvature of almost quaternion-Hermitian manifolds

Details Curvature of almost quaternion-Hermitian manifolds Curvature of almost quaternion-Hermitian manifolds

2007-08-02

arxiv.org/abs/0708.0309v1

Mathematics

Differential Geometry

40 pages

Scientific paper

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion \xi and its covariant derivative \widetilde\nabla\xi and determine relations between the decompositions of \xi\otimes\xi, \widetilde\nabla\xi and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.

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