Sasaki-Einstein空间$Y^{p,q}$中测地线的Toric数据、Killing形式和完全可积性
Toric data, Killing forms and complete integrability of geodesics in Sasaki-Einstein spaces $Y^{p,q}$
摘要：
本文证明了利用辛势和经典的Delzant构造可以得到5维Sasaki-Einstein空间$Y^{p,q}$上特殊Killing形式的完整列表.所得结果与直接计算所得结果一致，证明了该方法的可靠性，它实际上是复曲面Sasaki-Einstein流形的一种通用算法。最后讨论了测地线运动在$Y^{p,q}$空间中的可积性。
英文摘要：
In the present paper we show that the complete list of special Killing forms on the 5-dimensional Sasaki-Einstein spaces $Y^{p,q}$ can be extracted using the symplectic potential and the classical Delzant construction. The results achieved here agree with previous ones obtained by direct computation, proving the reliability of the method which stands in fact as a general algorithm for toric Sasaki-Einstein manifolds. Finally, we discuss the integrability of geodesic motion in $Y^{p,q}$ spaces.
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