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 2007

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Sectional Curvature
Compact Manifold
Nonnegative Curvature
Manifolds with Boundary
Ricci Curvature
Rigidity
Riemannian Manifold
Vanish
Metric

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Vanishing sectional curvature on the boundary and a conjecture of schroeder and strake. / Hang, Fengbo; Wang, Xiaodong.

In: Pacific Journal of Mathematics, Vol. 232, No. 2, 10.2007, p. 283-287.

Research output: Contribution to journalArticle

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