We prove that every conformal submersion from a round sphere onto an Einstein manifold with fibers being geodesics is—up to an isometry—the Hopf fibration composed with a conformal diffeomorphism of the complex projective space of appropriate dimension. We also show that there are no conformal submersions with minimal fibers between manifolds satisfying certain curvature assumptions.

中文翻译：

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关于具有测地线或最小纤维的保形浸没

我们证明了从圆形球体到以测地线为纤维的爱因斯坦流形上的每一次共形浸没——直到等距——由适当维数的复射影空间的共形微分同胚组成的 Hopf 纤维化。我们还表明，在满足某些曲率假设的流形之间没有具有最小纤维的保形浸没。