Closed characteristics on non-compact mechanical contact manifolds

Closed characteristics on non-compact mechanical contact manifolds
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非紧凑型机械接触流形的闭合特性

DOI：
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发表时间：
2013
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通讯作者：
R. Vandervorst
R. Vandervorst
中科院分区：
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文献类型：
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作者：
J. B. Berg;F. Pasquotto;T. O. Rot;R. Vandervorst

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研究了一类非紧切触流形：机械切触流形的闭特征的存在性。在[3]中证明了，在满足一定几何假设的条件下，R中的正则机械超曲面，特别是非紧机械超曲面，如果上半部分中的一个同调群不为零，则包含闭特征。本文通过黎曼流形余切丛的嵌入，将上述结果推广到非紧机械切触流形的情形。AMS科目：37J05，37J45，70H12。
This paper is concerned with the existence of closed characteristics for a class of non-compact contact manifolds: mechanical contact manifolds. In [3] it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in R, in particular non-compact ones, contain a closed characteristic if one homology group among the top half does not vanish. In the present paper, we extend the above mentioned existence result to the case of non-compact mechanical contact manifolds via embeddings in cotangent bundles of Riemannian manifolds. AMS Subject Class: 37J05, 37J45, 70H12.