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Almost Hermitian structures and quaternionic geometries

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  • Francisco Mart́n Cabrera, University of La Laguna
  • ,
  • Andrew Swann

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.

Original languageEnglish
JournalDifferential Geometry and its Application
Pages (from-to)199-214
Number of pages16
Publication statusPublished - 1 Sept 2004
Externally publishedYes

    Research areas

  • Almost hyper-Hermitian, Almost quaternion-Hermitian, Hyper-Kähler

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