论文标题
梯度缩小sasaki ricci solitons在sasakian dimension的sasakian歧管上最多七个
Gradient Shrinking Sasaki-Ricci Solitons on Sasakian Manifolds of Dimension Up to Seven
论文作者
论文摘要
在本文中，我们表明，沿sasaki-ricci沿sasaki ricci流动的均匀的l^4结合在紧凑的准式横向横向的fano sasakian（2n+1）-manifold M上，m是尺寸。极限空间上的独特单数Orbifold sasaki syiton在正常的投影品种上，在唯一的奇异kaehler-ricci soliton上是一个s^1-orbibundle，并具有两个环形象征性的两个orbifold奇异性。其次，对于n = 1，我们表明在紧凑的准规范的fano sasakian三尖口上只有两个非平凡的sasaki ricci soliton，其离开空间分别是泪滴和足球般的空间。对于n = 2,3，我们表明，如果m是横向k键，则sasaki ricci soliton是微不足道的。
In this paper, we show that the uniform L^4-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular transverse Fano Sasakian (2n+1)-manifold M. When M is dimension up to seven and the space of leaves of the characteristic foliation is well-formed, we first show that any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold Sasaki-Ricci soliton on the limit space which is a S^1-orbibundle over the unique singular Kaehler-Ricci soliton on a normal projective variety with codimension two orbifold singularities. Secondly, for n=1, we show that there are only two nontrivial Sasaki-Ricci solitons on a compact quasi-regular Fano Sasakian three-sphere with its leave space a teardrop-like and football-like space, respectively. For n=2,3, we show that the Sasaki-Ricci soliton is trivial one if M is transverse K-stable.
