| A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS |
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| 引用本文： | Zhu Da xin. A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS[J]. 数学年刊B辑(英文版), 1994, 15(3): 293-298 |
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| 作者姓名： | Zhu Da xin |
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| 作者单位： | Department of Mathematics，Tianjin Universityl Tianjin 300072，China. |
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| 摘 要： | ＡＣＯＭＰＬＥＴＥＭＥＴＲＩＣＯＦＰＯＳＩＴＩＶＥＣＵＲＶＡＴＵＲＥＯＮＲ~ｎＡＮＤＥＸＩＳＴＥＮＣＥＯＦＣＬＯＳＥＤＧＥＯＤＥＳＩＣＳ￥ＺＨＵＤＡＸＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｌＴｉａｎｊ?..
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| 关 键 词： | 正曲率 完全标准 测地学 黎曼流形 汉密尔顿系统 |
| 收稿时间： | 1992-03-29 |
| 修稿时间： | 1993-07-25 |
A COMPLETE METRIC OF POSITIVE CURVATUREON Rn AND EXISTENCE OF CLOSED GEODESICS |
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| Zhu Da xin. A COMPLETE METRIC OF POSITIVE CURVATUREON Rn AND EXISTENCE OF CLOSED GEODESICS[J]. Chinese Annals of Mathematics,Series B, 1994, 15(3): 293-298 |
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| Authors: | Zhu Da xin |
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| Affiliation: | DepartmentofMathematics,TianjinUniversity,Tianjin300072,China |
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| Abstract: | An example of complete Riemannian metric of positive (or nonnagative) curvature on Resuch as aam = a(x)dx' is obtained by direct caculations. Furthermore, by using a geodesic convex condition and a theorem for complete noncompact Riemannian manifold, an existence resultof periodic solution of prescribed energy for a singular Handltonian system is also obtained. |
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| Keywords: | Positive curvature Complete metric Geodesic Riemannian manifold Hamiltonian system. |
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