We investigate Jacobi fields and conjugate points in the context of sprays. We first prove that the conjugate points of a spray remain preserved under a projective change. Then, we establish conditions on the projective factor, so that the projectively deformed spray meets the conditions of a proposition that ensures the existence of conjugate points. We discuss our methods by means of illustrative examples, throughout the paper.

中文翻译：

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射流射流类的Jacobi场和共轭点

我们在喷雾的背景下研究雅可比场和共轭点。我们首先证明喷雾的共轭点在投影变化下保持不变。然后，我们在射影因子上建立条件，以使射影变形的喷雾满足确保共轭点存在的命题的条件。在整篇文章中，我们将通过说明性示例来讨论我们的方法。