Geodesic
Isotropic almost complex structures and harmonic unit vector fields
Archivum mathematicum, Tome 54 (2018) no. 1, pp. 15-32 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2018-1-15
Classification : 53C15, 53C43
Keywords: complex structures; energy functional; isotropic almost complex structure; unit tangent bundle; variational problem; tension field 
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Baghban, Amir; Abedi, Esmaeil. Isotropic almost complex structures and harmonic unit vector fields. Archivum mathematicum, Tome 54 (2018) no. 1, pp. 15-32. doi: 10.5817/AM2018-1-15

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