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Keywords
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complex structures, energy functional, isotropic almost complex
structure, unit tangent bundle, variational problem, tension field.
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Abstract
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Isotropic almost complex structures J, define a class of Riemannian
metrics g, on tangent bundles of Riemannian manifolds which
are a generalization of the Sasaki metric. In this paper, some results will
be obtained on the integrability of these almost complex structures and the
notion of a harmonic unit vector field will be introduced with respect to the
metrics g,0. Furthermore, the necessary and sufficient conditions for a unit
vector field to be a harmonic unit vector field will be obtained.
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