Vanishing sectional curvature on the boundary and a conjecture of schroeder and strake

Fengbo Hang, Xiaodong Wang

Research output: Contribution to journalArticle

Abstract

We prove some rigidity results for compact manifolds with boundary. For a compact Riemannian manifold with nonnegative Ricci curvature and simply connected mean convex boundary, we show that if the sectional curvature vanishes on the boundary, the metric must be flat.

Original languageEnglish (US)
Pages (from-to)283-287
Number of pages5
JournalPacific Journal of Mathematics
Volume232
Issue number2
DOIs
StatePublished - Oct 1 2007

Keywords

  • Mean convex boundary
  • Nonnegative Ricci curvature
  • Reilly's formula
  • Rigidity

ASJC Scopus subject areas

  • Mathematics(all)

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