Weyl structures on quaternionic manifolds. A state of the art

Details Weyl structures on quaternionic manifolds. A state of the art Weyl structures on quaternionic manifolds. A state of the art

2001-05-05

arxiv.org/abs/math/0105041v1

Mathematics

Differential Geometry

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Scientific paper

This is a survey on quaternion Hermitian Weyl (locally conformally quaternion K\"ahler) and hyperhermitian Weyl (locally conformally hyperk\"ahler) 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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