Sasaki-Einstein空间$T^{1,1}$上可分解锥上测地流的可积性
Integrability of the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$
摘要：
本文应用Hamilton动力学方法研究了Sasaki-Einstein空间$T^{1,1}$上可分解锥上的测地线流。在五维Sasaki-Einstein空间$T^{1,1}$及其Calabi-Yau度量锥中，明确地构造了运动常数，并证明了测地线的完全可积性.度量锥顶点处的奇异性可以用两种不同的方法平滑掉。使用小分辨率的测地线运动的解决锥仍然完全可积。相反，在圆锥形变形的情况下，完全可积性丧失。
英文摘要：
Methods of Hamiltonian dynamics are applied to study the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$. We construct explicitly the constants of motion and prove complete integrability of geodesics in the five-dimensional Sasaki-Einstein space $T^{1,1}$ and its Calabi-Yau metric cone. The singularity at the apex of the metric cone can be smoothed out in two different ways. Using the small resolution the geodesic motion on the resolved conifold remains completely integrable. Instead, in the case of the deformation of the conifold the complete integrability is lost.
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