On harmonic vector fields.

@article{Konderak1992,
abstract = {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 + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.},
author = {Konderak, Jerzy J.},
journal = {Publicacions Matemàtiques},
keywords = {Variedad riemanniana; Espacio fibrado; Aplicaciones; Tensor métrico; Sasakian metric; harmonic mappings; pseudo-Riemannian manifold},
language = {eng},
number = {1},
pages = {217-228},
title = {On harmonic vector fields.},
url = {http://eudml.org/doc/41156},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Konderak, Jerzy J.
TI - On harmonic vector fields.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 217
EP - 228
AB - 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 + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.
LA - eng
KW - Variedad riemanniana; Espacio fibrado; Aplicaciones; Tensor métrico; Sasakian metric; harmonic mappings; pseudo-Riemannian manifold
UR - http://eudml.org/doc/41156
ER -