JournalscmhVol. 79 , No. 2DOI 10.1007/s00014-004-0803-3

Families of strong KT structures in six dimensions

  • Anna Fino

    Università degli Studi di Torino, Italy
  • Simon Salamon

    King's College London, UK
  • Maurizio Parton

    Università di Chieti-Pescara, Italy
Families of strong KT structures in six dimensions cover

Abstract

This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=\Ga\bsGM=\Ga\bs G for which the fundamental 2-form is \pd\opd\pd\opd-closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limaçon-shaped curve in the complex plane. Related theory is used to provide examples of various types of Ricci-flat structures.