| 夏大峰,徐森林,祁锋.非正截曲率的完备Riemann流形在无穷远截曲率趋于零的条件[J].数学研究及应用,1999,19(4):747~752 |
| 非正截曲率的完备Riemann流形在无穷远截曲率趋于零的条件 |
| Condition of Sectional Curvature Tend to Zero at to infinity about Complete Riemannian Manifold with Non-Positive Curvature |
| 投稿时间：1997-06-09 |
| DOI：10.3770/j.issn:1000-341X.1999.04.023 |
| 中文关键词: 正规测地线 Jaboci场 截曲率 |
| 英文关键词:normal geodesic Jacobi field sectional curvature. |
| 基金项目: |
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| 中文摘要: |
| 本文给出并证明了定理；设Ｍ为具非正截曲率的完备Ｒｉｅｍａｎｎ流形，Ｔ：［０，＋∞）→Ｍ为Ｍ上的正规测地线，Ｕ是沿Ｔ且初值为零的非平凡正常Ｊａｃｏｂｉ场，若存在ａ＞０，ｔ０＞０，使得当ｔ≥ｔ０时． |
| 英文摘要: |
| In this paper, we give and prove the following theorem: If M is a complete Riemannian manifold with non-positive curvature, r: [0,+∞ )→M be a normal geodesic on M, U bea non-trivial normal Jacobi field along r and U (0) = 0, and if there is a a> 0,t０>0 so that(?). |
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