论文标题
尺寸简单连接的流形$ 6K $的正率曲率的指标
Metrics of Positive Ricci Curvature on Simply-Connected Manifolds of Dimension $6k$
论文作者
论文摘要
Gromov和Lawson的手术定理的结果是，每个封闭的，简单地连接的6个Manifold都承认了阳性标态曲率的Riemannian指标。对于阳性RICCI曲率的指标，是否存在类似结果，这是广泛开放的。对于那些歧管的那些歧管，尚无障碍，可以承认阳性曲率的度量，而已知的示例数量有限。在本文中，我们介绍了通过标记的两分图的某些$ 6K $维歧管的新描述，并使用作者的早期结果来构建在这些歧管上的正ricci曲率指标。通过这种方式，我们获得了许多新的示例，包括旋转和非自旋的$ 6K $维歧管，并具有带正面的RICCI曲率度量。
A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply-connected 6-manifold admits a Riemannian metric of positive scalar curvature. For metrics of positive Ricci curvature it is widely open whether a similar result holds; there are no obstructions known for those manifolds to admit a metric of positive Ricci curvature, while the number of examples known is limited. In this article we introduce a new description of certain $6k$-dimensional manifolds via labeled bipartite graphs and use an earlier result of the author to construct metrics of positive Ricci curvature on these manifolds. In this way we obtain many new examples, both spin and non-spin, of $6k$-dimensional manifolds with a metric of positive Ricci curvature.
