Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature

Qilin Yang

Colloquium Mathematicae (2009)

  • Volume: 114, Issue: 2, page 277-289
  • ISSN: 0010-1354

Abstract

top
It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are Kähler; the results obtained are optimal.

How to cite

top

Qilin Yang. "Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature." Colloquium Mathematicae 114.2 (2009): 277-289. <http://eudml.org/doc/284370>.

@article{QilinYang2009,
abstract = {It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are Kähler; the results obtained are optimal.},
author = {Qilin Yang},
journal = {Colloquium Mathematicae},
keywords = {harmonic map; Kähler manifold; strongly seminegative curvature},
language = {eng},
number = {2},
pages = {277-289},
title = {Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature},
url = {http://eudml.org/doc/284370},
volume = {114},
year = {2009},
}

TY - JOUR
AU - Qilin Yang
TI - Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 2
SP - 277
EP - 289
AB - It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are Kähler; the results obtained are optimal.
LA - eng
KW - harmonic map; Kähler manifold; strongly seminegative curvature
UR - http://eudml.org/doc/284370
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.