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

• Autorzy: Qilin Yang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C43: Differential geometric aspects of harmonic maps
• 58E20: Harmonic maps , etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 114
• Numer: 2
• Strony: 277-289

Daty

wydano

2009

Twórcy

autor

Qilin Yang

• Mathematical Department, Tsinghua University, 100084, Beijing, P.R. China
• Graduate School of Mathematics, Nagoya University Chikusa-ku, Nagoya 464-8602, Japan

Identyfikatory

DOI

10.4064/cm114-2-9