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 language | English |
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Pages (from-to) | 131-151 |
Number of pages | 20 |
Journal | Geometriae Dedicata |
Volume | 123 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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