elliptic and hyperbolic closed geodesic 椭圆与双曲闭测地线
To be precise, we proved the following two results:Theorem1 Let M~n be a complete noncompact manifold with nonnegative curvature. If M~n contains a nontrivial closed geodesic (i. e. not apoint), thenα_M =0.
具体来讲，我们证明了下面两个定理：定理1设M~n为完备非紧非负曲率流形，若M~n含有—非平凡的闭测地线(即不是一个点)，则必有α_M=0。
参考来源 - 具有非负曲率完备非紧流形的体积增长·2,447,543篇论文数据，部分数据来源于NoteExpress
以上来源于: WordNet
The necessary condition of external oscillations is the existence of closed geodesic lines on the surface of scatterers.
外部振荡存在的必要条件是散射体表面有闭合测地线。
The existence of closed geodesic lines (oscillate loci) is proved. Although there are infinite closed loci on the surface of scatterer, they yield same result in determining SEM poles.
本文给出了闭合测地线，即振荡轨迹的存在性，证明了这种闭合轨迹虽有无穷多条，但就确定SEM极点来说是等价的。
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