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SPHERE THEOREM FOR MANIFOLDS WITH POSITIVE CURVATURE

2006
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Glasgow Mathematical Journal
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In this paper, we prove that, for any integer n ≥ 2, and any δ > 0 there exists an (n, δ) ≥ 0 such that if M is an n-dimensional complete manifold with sectional curvature K M ≥ 1 and if M has conjugate radius ρ ≥ π 2 + δ and contains a geodesic loop of length 2(π − (n, δ)) then M is diffeomorphic to the Euclidian unit sphere ޓ n . 2002 Mathematics Subject Classification. 53C20, 53C21. Introduction. One of the fundamental problems in Riemannian geometry is to determine the relation between

doi:10.1017/s0017089505002843
fatcat:cmxu7obqlzhungwljwgcg6a4gm