论文标题
Bismut ricci扁平歧管与对称性
Bismut Ricci flat manifolds with symmetries
论文作者
论文摘要
我们构建了紧凑的统一riemannian歧管的例子，该歧管承认不变的bismut连接是ricci平坦且非平坦的，以这种方式证明了广义的Alekseevsky-Kimelfeld定理不存在。还提供了紧凑型均匀的Bismut ricci扁平空间的分类$ 5 $。此外，我们研究了没有琐碎的第三次贝蒂数的紧凑型同质空间，并指出了构造bismut ricci平坦歧管的其他可能方法。最后，由于Bismut Ricci平坦连接对应于广义RICCI流的固定点，因此我们讨论了流动下某些示例的稳定性。
We construct examples of compact homogeneous Riemannian manifolds admitting an invariant Bismut connection that is Ricci flat and non-flat, proving in this way that the generalized Alekseevsky-Kimelfeld theorem does not hold. The classification of compact homogeneous Bismut Ricci flat spaces in dimension $5$ is also provided. Moreover, we investigate compact homogeneous spaces with non trivial third Betti number, and we point out other possible ways to construct Bismut Ricci flat manifolds. Finally, since Bismut Ricci flat connections correspond to fixed points of the generalized Ricci flow, we discuss the stability of some of our examples under the flow.
