Address: Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, Tabriz 53751 71379, Iran
E-mail:
amirbaghban87@gmail.com
esabedi@azaruniv.ac.ir
Abstract: 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.
AMSclassification: primary 53C43; secondary 53C15.
Keywords: complex structures, energy functional, isotropic almost complex structure, unit tangent bundle, variational problem, tension field.
DOI: 10.5817/AM2018-1-15