关于Rn中星形曲线的几何

Pub Date : 2019-01-01 DOI:10.2206/kyushujm.73.123

Stefan A. HOROCHOLYN

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引用次数: 0

摘要

。利用向量束上的连接理论和循环D模，研究了R n中星形曲线的流形M。定义了M上的“积分曲线”(即某些可容许变形)的适当概念，并通过等谱流对可容许变形的结果空间进行分类，这些空间由n -KdV (Korteweg-de Vries)层次中的方程描述。

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ON THE GEOMETRY OF STAR-SHAPED CURVES IN Rn

. The manifold M of star-shaped curves in R n is considered via the theory of connections on vector bundles, and cyclic D -modules. The appropriate notion of an ‘integral curve’ (i.e. certain admissible deformations) on M is deﬁned, and the resulting space of admissible deformations is classiﬁed via iso-spectral ﬂows, which are shown to be described by equations from the n -KdV (Korteweg–de Vries) hierarchy.

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