Harmonicity of unit vector fields with respect to a class of Riemannian metrics

2014/12/07 by Amir Baghban, Baghban, A., Esmaeil Abedi +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1412.2346

openalex publication_date 2014/12/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The isotropic almost complex structures induce a Riemannian metric g_δ,σ on TM, which are the generalized type of Sasakian metric. In this paper, the Levi-Civita connection of g_δ,σ is calculated and the harmonicity of unit vector fields from (M, g) to (S(M), i*g_δ,0) is investigated, where i*g_δ,0 is a particular type of induced metric i*g_δ,σ. Finally, an important example is presented which satisfies in main theorem of the paper.

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