| ON THE SECTIONAL CURVATURE OF A RIEMANNIAN MANIFOLD |
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| 引用本文： | Bai Zhengguo(白正国. ON THE SECTIONAL CURVATURE OF A RIEMANNIAN MANIFOLD[J]. 数学年刊B辑(英文版), 1990, 11(1): 70-73 |
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| 作者姓名： | Bai Zhengguo(白正国 |
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| 作者单位： | Dedicated to |
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| 基金项目： | Projects Supported by the Natural Science Funds of china. |
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| 摘 要： | In this paper the author establishes the following1.If M~n(n≥3)is a connected Riemannian manifold,then the sectional curvatureK(p),where p is any plane in T~x(M),is a function of at most n(n-1)/2 variables.Moreprecisely,K(p)depends on at most n(n-1)/2 parameters of group SO(n).2.Lot M~n(n≥3)be a connected Riemannian manifold.If there exists a point x ∈ Msuch that the sectional curvature K(p)is independent of the plane p∈T_x(M),then M is aspace of constant curvature.This latter improves a well-known theorem of F.Schur.
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| 收稿时间： | 1989-04-06 |
On the Sectional Curvature of a Riemannian Manifold |
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| Affiliation: | Department of Mathematics, Hangzhou University, Hangzhou, Zhejiang, China. |
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