Almost Hermitian Structures and Quaternionic Geometries
Differential Geometry
2007-05-23 v1
Abstract
Gray & Hervella gave a classification of almost Hermitian structures (g,I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g,I,J,K). In general dimension we find at most 167 different almost hyper-Hermitian structures. In particular, we obtain a number of relations that give hyperK\"aher or locally conformal hyperK\"ahler structures, thus generalising a result of Hitchin. We also study the types of almost quaternion-Hermitian geometries that arise and tabulate the results.
Cite
@article{arxiv.math/0307118,
title = {Almost Hermitian Structures and Quaternionic Geometries},
author = {Francisco Martin Cabrera and Andrew Swann},
journal= {arXiv preprint arXiv:math/0307118},
year = {2007}
}
Comments
22 pages, 5 tables