In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D >= 7. The local construction involves taking a circle bundle over a (D - I)-dimensional Einstein-Kahler metric that is itself constructed as a complex line bundle over a product of Einstein-Kahler spaces. In general, the resulting Einstein-Sasaki spaces are singular, but if parameters in the local solutions satisfy appropriate rationality conditions, the metrics extend smoothly onto complete and non-singular compact manifolds. The seven-dimensional space, whose base is a complex line bundle over S-2 X S-2, is discussed in detail since it has relevance in terms of the AdS/CFT correspondence.
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机译：在本文中，我们获得维D> = 7的新非奇异Einstein-Sasaki空间。局部构造涉及在（D-I）维Einstein-Kahler度量上取一个圆束，该E本身被构造为复线捆绑在一个Einstein-Kahler空间的乘积上。通常，所得的Einstein-Sasaki空间是奇异的，但是，如果局部解中的参数满足适当的合理性条件，则度量将平滑地扩展到完整和非奇异的紧流形上。七维空间的基础是在S-2 X S-2上的复数线束，因此将对其进行详细讨论，因为它在AdS / CFT对应方面具有相关性。
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