Almost Hermitian Structures and Quaternionic Geometries

Details Almost Hermitian Structures and Quaternionic Geometries Almost Hermitian Structures and Quaternionic Geometries

2003-07-09

arxiv.org/abs/math/0307118v1

Mathematics

Differential Geometry

22 pages, 5 tables

Scientific paper

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.

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