Almost Hermitian structures and quaternionic geometries

TY - JOUR

T1 - Almost Hermitian structures and quaternionic geometries

AU - Mart́n Cabrera, Francisco

AU - Swann, Andrew

PY - 2004/9/1

Y1 - 2004/9/1

N2 - Gray and 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 hyper-Kähler or locally conformal hyper-Kähler structures, thus generalising a result of Hitchin. We also study the types of almost quaternion-Hermitian geometries that arise and tabulate the results.

AB - Gray and 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 hyper-Kähler or locally conformal hyper-Kähler structures, thus generalising a result of Hitchin. We also study the types of almost quaternion-Hermitian geometries that arise and tabulate the results.

KW - Almost hyper-Hermitian

KW - Almost quaternion-Hermitian

KW - Hyper-Kähler

UR - http://www.scopus.com/inward/record.url?scp=3242784878&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2004.03.008

DO - 10.1016/j.difgeo.2004.03.008

M3 - Journal article

AN - SCOPUS:3242784878

SN - 0926-2245

VL - 21

SP - 199

EP - 214

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

IS - 2

ER -