The identification of conformal hypercomplex and quaternionic manifolds
摘要
We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by `\xi transformations', relating connections on quaternionic manifolds, and a new type `\hat\xi transformations' relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds.
引用
@article{arxiv.math/0512084,
title = {The identification of conformal hypercomplex and quaternionic manifolds},
author = {Eric Bergshoeff and Stefan Vandoren and Antoine Van Proeyen},
journal= {arXiv preprint arXiv:math/0512084},
year = {2015}
}
备注
22 pages, 2 figures, Contribution to the proceedings volume for the Conference "Symmetry in Geometry and Physics" in honour of Dmitri Alekseevsky, September 2005