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| On the Sectional Curvature of a Riemannian Manifold |
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Citation： |
Bai Zhengguo(白正国).On the Sectional Curvature of a Riemannian Manifold[J].Chinese Annals of Mathematics B,1990,11(1):70~73 |
| Page view： 809
Net amount： 693 |
Authors： |
Bai Zhengguo(白正国); |
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| Abstract： |
In this papor the author establishes the following
1. If llln(w>‘3) is a cohneeted. Kieinanniah manifold, then the sectional curvature K(p), where p is any plane in T_x(M), is a function of at most n(n-1)/2 variables. More precisely, K(p) depends on at most n(n-l)/2 parameters of group SO(n).
2. Lot M^n(n\leq 3) be a connected Riemannian manifold. If there exists a point x \in M such that the sectional curvature K(p) is-independent of the plane p\in T_x(M), then M is a space of constant curvature.
This latter improves a well-known theorem of F. Schur. |
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