Title: The map between conformal hypercomplex/hyper-Kähler and quaternionic(-Kähler) geometry
Authors: Bergshoeff, E ×
Cucu, S
de Wit, T
Gheerardyn, J
Vandoren, S
Van Proeyen, Antoine #
Issue Date: Mar-2006
Publisher: Springer-Verlag Heidelberg
Series Title: Communications in mathematical physics vol:262 issue:2 pages:411-457
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-Kahler manifolds is mapped to quaternionic-Kahler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.
ISSN: 0010-3616
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Theoretical Physics Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science