Harmonic Almost Contact Structures

2 3 Fe b 20 06 HARMONIC ALMOST CONTACT STRUCTURES

An almost contact metric structure is parametrized by a section σ of an associated homogeneous fibre bundle, and conditions for σ to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field ξ, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for σ reduce to those for ξ, regarde...

Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras

We study almost contact metric structures on 5-dimensional nilpotent Lie algebras and investigate the class of left invariant almost contact metric structures on corresponding Lie groups. We determine certain classes that a five-dimensional nilpotent Lie group can not be equipped with.

Contact Structures and Harmonic Maps with Minimal Fibres

Almost harmonic spinors

We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends to zero. As an application, we compare the Dirac spectrum with the conformal volume. Spineurs presque harmoniques Résumé. Nous montrons que, sur toute variété spinorielle compacte sans bord non difféomorphe à la sphèr...

Superminimal fibres in an almost contact metric submersion

The superminimality of the fibres of an almost contact metric submersion is used to study the integrability of the horizontal distribution and the structure of the total space.