可积测地线流和多中心与Bianchi A度量
Integrable geodesic flows and Multi-Centre versus Bianchi A metrics
摘要：
它表明，大多数，但不是全部，四维度量的多中心家庭与可积测地线流可以被认为是属于空间齐次Bianchi型A度量。我们证明了任何对角双轴Bianchi II度量都有一个可积的测地线流，并且该族中最简单的超凯勒度量为其可观测量显示了一个有限维W-代数。我们的分析还提出了轻非对角线比安奇六$_0$和七$_0$指标，这似乎是新的。我们的结论表明，在文献中提倡的椭圆坐标不分离的三轴比安奇IX度规的哈密顿-雅可比方程。
英文摘要：
It is shown that most, but not all, of the four dimensional metrics in the Multi-Centre family with integrable geodesic flow may be recognized as belonging to spatially homogeneous Bianchi type A metrics. We show that any diagonal bi-axial Bianchi II metric has an integrable geodesic flow, and that the simplest hyperkähler metric in this family displays a finite dimensional W-algebra for its observables. Our analysis puts also to light non-diagonal Bianchi VI$_0$ and VII$_0$ metrics which seem to be new. We conclude by showing that the elliptic coordinates advocated in the literature do not separate the Hamilton-Jacobi equation for the tri-axial Bianchi IX metric.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
