Almost Quaternion-Hermitian Manifolds

Details Almost Quaternion-Hermitian Manifolds Almost Quaternion-Hermitian Manifolds

2002-06-11

arxiv.org/abs/math/0206115v3

Mathematics

Differential Geometry

25 pages

Scientific paper

Following the point of view of Gray and Hervella, we derive detailed conditions which characterize each one of the classes of almost quaternion-Hermitian $4n$-manifolds, $n>1$. Previously, by completing a basic result of A. Swann, we give explicit descriptions of the tensors contained in the space of covariant derivatives of the fundamental form $\Omega$ and split the coderivative of $\Omega$ into its ${\sl Sp}(n){\sl Sp}(1)$-components. For $4n>8$, A. Swann also proved that all the information about the intrinsic torsion $\nabla \Omega$ is contained in the exterior derivative ${\sl d} \Omega$. Thus, we give alternative conditions, expressed in terms of ${\sl d} \Omega$, to characterize the different classes of almost quaternion-Hermitian manifolds.

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