English

RC-positivity and rigidity of harmonic maps into Riemannian manifolds

Differential Geometry 2018-09-13 v1

Abstract

In this paper, we show that every harmonic map from a compact K\"ahler manifold with uniformly RC-positive curvature to a Riemannian manifold with non-positive complex sectional curvature is constant. In particular, there is no non-constant harmonic map from a compact K\"ahler manifold with positive holomorphic sectional curvature to a Riemannian manifold with non-positive complex sectional curvature.

Keywords

Cite

@article{arxiv.1809.04449,
  title  = {RC-positivity and rigidity of harmonic maps into Riemannian manifolds},
  author = {Jun Wang and Xiaokui Yang},
  journal= {arXiv preprint arXiv:1809.04449},
  year   = {2018}
}