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• W2055062282 abstract "We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killing vector) and quaternionic manifolds of one quaternionic dimension less. An important role is played by 'xi-transformations', relating complex structures on conformal hypercomplex manifolds and connections on quaternionic manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other." @default.
• W2055062282 created "2016-06-24" @default.
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• W2055062282 date "2005-12-20" @default.
• W2055062282 modified "2023-09-27" @default.
• W2055062282 title "The Map Between Conformal Hypercomplex/ Hyper-Kähler and Quaternionic(-Kähler) Geometry" @default.
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• W2055062282 doi "https://doi.org/10.1007/s00220-005-1475-6" @default.
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