English

New gap theorem on complete Riemannian manifolds

Differential Geometry 2013-01-08 v2 Analysis of PDEs

Abstract

In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is Ricci flat.

Keywords

Cite

@article{arxiv.math/0605360,
  title  = {New gap theorem on complete Riemannian manifolds},
  author = {Qi-hua Ruan},
  journal= {arXiv preprint arXiv:math/0605360},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to some crucial errors

R2 v1 2026-07-22T17:35:49.696Z