In this article we introduce a hyperbolic metric on the (normalized) space ofstability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X)=1$. And we show that all walls are geodesic in the normalized space withrespect to the hyperbolic metric. Furthermore we demonstrate how the hyperbolicmetric is helpful for us by discussing mainly three topics. We first make astudy of so called Bridgeland's conjecture. In the second topic we prove afamous Orlov's theorem without the global Torelli theorem. In the third topicwe give an explicit example of stable complexes in large volume limits by usingthe hyperbolic metric. Though Bridgeland's conjecture may be well-known foralgebraic geometers, we would like to start from the review of it.
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机译：在本文中，我们介绍了在Picard等级$ \ rho（X）= 1 $的射影K3曲面$ X $上的（规范化）稳定性条件空间上的双曲度量。并且我们证明，相对于双曲度量，所有墙在规范化空间中都是测地线。此外，我们主要通过讨论三个主题来证明双曲线对我们有何帮助。我们首先对所谓的布里奇兰猜想进行研究。在第二个主题中，我们证明了著名的Orlov定理，而没有全局Torelli定理。在第三个主题中，我们通过使用双曲度量给出了在大体积限制下稳定络合物的明确示例。尽管布里奇兰的猜想可能是众所周知的代数几何，但我们还是要从对其进行回顾开始。
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