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Isotropic almost complex structures and harmonic unit vector fields. (English) Zbl 1424.53098

Summary: Isotropic almost complex structures \(J_{\delta,\sigma}\) define a class of Riemannian metrics \(g_{\delta,\sigma}\) 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 \(g_{\delta,0}\). Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.

MSC:

53C43 Differential geometric aspects of harmonic maps
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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