黎曼扭曲通量管中的Ricci曲率和测地线流稳定性
Ricci curvature and geodesic flows stability in Riemannian twisted flux tubes
摘要：
计算了黎曼流形中扭曲通量管的Ricci曲率和截面曲率，研究了扭曲通量管的稳定性。测地线方程用于表明，在厚管的情况下，平面（弗伦内无扭）管的曲率具有阻尼沿管的流速的效果ct。本文用不稳定流的负截面曲率方法研究了黎曼扭曲细管（几乎是细丝）中测地线流对常径向扰动的稳定性。没有象贝尔特拉米流那样的特殊形式的流动被承认，并且证明对于细管的情况是一般的。据发现，对于正扰动和角速度的流动，不稳定性实现，因为截面Ricci曲率的扭曲管度规是负的。
英文摘要：
Ricci and sectional curvatures of twisted flux tubes in Riemannian manifold are computed to investigate the stability of the tubes. The geodesic equations are used to show that in the case of thick tubes, the curvature of planar (Frenet torsion-free) tubes have the effect ct of damping the flow speed along the tube. Stability of geodesic flows in the Riemannian twisted thin tubes (almost filaments), against constant radial perturbations is investigated by using the method of negative sectional curvature for unstable flows. No special form of the flow like Beltrami flows is admitted, and the proof is general for the case of thin tubes. It is found that for positive perturbations and angular speed of the flow, instability is achieved, since the sectional Ricci curvature of the twisted tube metric is negative.
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