We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.
Original languageEnglish
Pages (from-to)347-351
Number of pages5
JournalGeometriae Dedicata
Volume203
Issue number1
DOIs
StatePublished - 1 Dec 2019

    Research areas

  • Comparison geometry, Differential geometry, Metric geometry, Optimal transport, Rigidity

ID: 126316067