On harmonic vector fields

J. J. Konderak
1992 Publicacions matemàtiques  
ON HARMONIC VECTOR FIELDS JERZY J . KONDERAK A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics . We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel . We also consider the metrics II and I + 17 on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them .
doi:10.5565/publmat_36192_17 fatcat:nojufmjjxzfpzjjglpdddurkuq