Vol. 282, No. 2, 2016

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On Blaschke's conjecture

Xiaole Su, Hongwei Sun and Yusheng Wang

Vol. 282 (2016), No. 2, 479–485
Abstract

Blaschke’s conjecture asserts that if a complete Riemannian manifold M satisfies diam(M) = Inj(M) = π 2 , then M is isometric to Sn(1 2) or to the real, complex, quaternionic or octonionic projective plane with its canonical metric. We prove that the conjecture is true under the assumption that secM 1.

Keywords
Blaschke's conjecture, Berger's rigidity theorem, Toponogov's comparison theorem
Mathematical Subject Classification 2010
Primary: 53C20
Milestones
Received: 11 June 2015
Accepted: 19 December 2015
Published: 3 March 2016
Authors
Xiaole Su
School of Mathematical Sciences
Beijing Normal University
Beijing, 100875
China
Hongwei Sun
School of Mathematical Sciences
Capital Normal University
Beijing, 100037
China
Yusheng Wang
School of Mathematical Sciences
Beijing Normal University
Beijing, 100875
China