Almost Hermitian Structures and Quaternionic Geometries

2003/07/09 by Francisco Martin Cabrera, Andrew Swann, Cabrera, Francisco Martin +1
Mathematics · #53C10 #53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C10 #msc:53C15 #msc:53C25

paper · pdf · doi:10.48550/arxiv.math/0307118

22 pages, 5 tables

arxiv created 2003/07/09 · arxiv updated 2009/12/01

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 hyperKäher or locally conformal hyperKähler 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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