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Keywords:
complex structures; energy functional; isotropic almost complex structure; unit tangent bundle; variational problem; tension field
complex structures; energy functional; isotropic almost complex structure; unit tangent bundle; variational problem; tension field
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.
References:
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