Weyl structures on quaternionic manifolds. A state of the art

Abstract

This is a survey on quaternion Hermitian Weyl (locally conformally quaternion Kähler) and hyperhermitian Weyl (locally conformally hyperkähler) manifolds. These geometries appear by requesting the compatibility of some quaternion Hermitian or hyperhermitian structure with a Weyl structure. The motivation for such a study is two-fold: it comes from the constantly growing interest in Weyl (and Einstein-Weyl) geometry and, on the other hand, from the necessity of understanding the existing classes of quaternion Hermitian manifolds.

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References in corpus (2)

• Geometry of Hyper-Kähler Connections with Torsion
• Geometry of Quaternionic Kähler connections with torsion

Cited by in corpus (8)

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• Quaternion CR-submanifolds of a Locally Conformal Quaternion Kaehler Manifold
• Hyperkaehler manifolds with torsion obtained from hyperholomorphic bundles