On harmonic vector fields.

Jerzy J. Konderak

Publicacions Matemàtiques (1992)

  • Volume: 36, Issue: 1, page 217-228
  • ISSN: 0214-1493

Abstract

top
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.

How to cite

top

Konderak, Jerzy J.. "On harmonic vector fields.." Publicacions Matemàtiques 36.1 (1992): 217-228. <http://eudml.org/doc/41156>.

@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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.