We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we provide an improved example which shows that the claim in our title is nevertheless true.

中文翻译：

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并非半黎曼测地的每个共轭点都是分叉点

我们回顾一下Musso，Pejsachowicz和Portaluri在2007年讨论的半黎曼测地线的示例，以表明并非每个共轭点都是分叉点。我们在他们的论证中指出了一个错误，表明在该测地线上实际上每个共轭点都是一个分叉点。最后，我们提供了一个改进的示例，该示例表明标题中的声明仍然是正确的。