关于Petersen-Wilhelm猜想的注记
A note on the Petersen-Wilhelm conjecture
摘要：
在这篇注记中，我们考虑从紧流形，同伦等价于正曲率的Bazaikin空间或Escherenburg空间的浸没。我们表明，如果浸没是非平凡的，基地的尺寸是大于的纤维的尺寸。与以前的结果一起，证明了Petersen-Wilhelm猜想对于所有已知的正曲率紧致流形。
英文摘要：
In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm Conjecture for all the known compact manifolds with positive curvature.
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