标题： 非正曲率黎曼流形上遍历测度的普遍性的一个新条件 显示英文标题

标题： A new condition for the genericity of ergodic measures on non-positively curved Riemannian manifolds

摘要： 本文研究了非正曲率黎曼流形上的测地流的遍历概率测度的普遍性。 我们证明了存在一个乘积流形的开等距嵌入，其中有一个因子与$S^1$等距，这表明遍历测度集合的闭包不包含所有不变测度，因此遍历概率测度的普遍性失效。 我们的结果显著回答了一个关于 Heintze 所提出的特定 3-流形的例子的开放问题。 显示英文摘要

摘要： This article investigates the genericity of ergodic probability measures for the geodesic flow on non-positively curved Riemannian manifolds. We demonstrate that the existence of an open isometric embedding of a product manifold with a factor isometric to $S^1$ implies that the closure of the set of ergodic measures does not encompass all invariant measures, thus the genericity of ergodic probability measures fails. Our findings notably provide an answer to an open question concerning a specific example of 3-manifold attributed to Heintze.