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KMID : 0368019910140010099
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Journal of Soonchunhyang University
1991 Volume.14 No. 1 p.99 ~ p.102
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A Note on manifolds of Positive Ricci Curvature
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Abstract
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Let M be a compact Riemannian man with positive Ricci curvature normalized by Ric_(M)≥n-1
According to Bishop´s volumn comparison theorem, the volume of M satisfies vol(M)≤w_(n), where w_(n) denotes the volumne of S^(n), and the equality holds if and only if M is isometric to S^(n).
Is M topologically similar to S^(n) when vol(M) is close to w_(n)?
In this note we construct a diffeomorphism between M and S^(n) with Lipso??ity constant close to one.
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KEYWORD
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