Harmonic almost contact structures

Esther Vergara-Diaz, C.M. Wood

Research output: Contribution to journalArticlepeer-review

Abstract

An almost contact metric structure is parametrized by a section sigma of an associated homogeneous fibre bundle, and conditions for sigma to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field xi, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for sigma reduce to those for xi, regarded as a section of the unit tangent bundle. These include trans-Sasakian structures. On the other hand, there are examples where xi is harmonic but sigma is not a harmonic section. Many examples arise by considering hypersurfaces of almost Hermitian manifolds, with the induced almost contact structure, and comparing the harmonic section equations for both structures.

Original languageEnglish
Pages (from-to)131-151
Number of pages20
JournalGeometriae Dedicata
Volume123
Issue number1
DOIs
Publication statusPublished - Dec 2006

Keywords

  • harmonic section
  • harmonic map
  • harmonic unit vector field
  • harmonic almost complex structure
  • almost contact metric structure
  • trans-Sasakian
  • nearly cosymplectic
  • nearly Sasakian
  • nearly Kahler structure
  • ALMOST-COMPLEX STRUCTURES
  • TRANS-SASAKIAN MANIFOLDS
  • HOPF VECTOR-FIELDS
  • RIEMANNIAN-MANIFOLDS
  • ENERGY
  • VOLUME
  • DISTRIBUTIONS
  • 3-MANIFOLDS

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