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| A COMPLETE METRIC OF POSITIVE CURVATUREON Rn AND EXISTENCE OF CLOSED GEODESICS |
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Citation： |
Zhu Da xin.A COMPLETE METRIC OF POSITIVE CURVATUREON Rn AND EXISTENCE OF CLOSED GEODESICS[J].Chinese Annals of Mathematics B,1994,15(3):293~298 |
| Page view： 978
Net amount： 535 |
Authors： |
Zhu Da xin; |
Foundation： |
Project supported by the National Natural Science Foundation of China. |
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| Abstract： |
An example of complete Riemannian metric of positive (or nonnagative) curvature on Rn
such as $ds^{2}=a(x)dx^{2}$ is obtained by direct caculations. Furthermore, by using a geodesic convex condition and a theorem for complete noncompact Riemannian manifold, an existence result
of periodic solution of prescribed energy for a singular Hamiltonian system is also obtained. |
Keywords： |
Positive curvature, Complete metric, Geodesic, Riemannian manifold,
Hamiltonian system. |
Classification： |
53C21 |
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