On the integrability of the isotropic almost complex structures and harmonic unit vector fields

2016/06/29 by Amir Baghban, Baghban, Amir, Esmaeil Abedi +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1606.09198

openalex publication_date 2016/06/29 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

Aguilar introduced isotropic almost complex structures J_{δ, σ} on the tangent bundle of a Riemannian manifold (M, g). In this paper, some results will be obtained on the integrability of these structures. These structures with the Liouville 1-form define a class of Riemannian metrics g_{δ, σ} on T M which are a generalization of the Sasaki metric. Moreover, the notion of a harmonic unit vector field is introduced with respect to these metrics like as the Sasaki metric and the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field are obtained.

Related

• Harmonicity of unit vector fields with respect to a class of Riemannian metrics
• Harmonic almost contact structures
• Harmonic sections of tangent bundles equipped with Riemannian g-natural metrics
• Curvatures of metrics induced by the isotropic almost complex structures
• Curvature and integrability of almost complex structures