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A GENERALIZATION OF AN INEQUALITY OF LI AND ZHONG, AND ITS GEOMETRIC APPLICATION
A GENERALIZATION OF AN INEQUALITY OF LI AND ZHONG, AND ITS GEOMETRIC APPLICATION
- 대한수학회
- Bulletin of the Korean Mathematical Society
- Vol.20 No.1
-
1983.0151 - 54 (4 pages)
- 0
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Let M be a n-dimensional compact Riemannian manifold with sectional curvature bounded below by one. Then Li and Zhong[3], and Li and Treibergs [4] proved that if the first eigenvalue of the Laplacian .lambda.$_{1}$ is less than some universal constant and if n.leq.4, then M is diffeomorphic to the n-sphere S$^{n}$ . The purpose of this paper is to prove this pinching theorem for all n with some extra condition.
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