Year: 2025
Author: Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu
Journal of Mathematical Study, Vol. 58 (2025), Iss. 1 : pp. 38–61
Abstract
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 $M.$ Then we are able to study the structure of the limit space. As consequences, when $M$ is of dimension five and the space of leaves of the characteristic foliation is of type I, any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold Sasaki-Ricci soliton and is trivial one if $M$ is transverse $K$-stable. Note that when the characteristic foliation is of type II, the same estimates hold along the conic Sasaki-Ricci flow.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v58n1.25.03
Journal of Mathematical Study, Vol. 58 (2025), Iss. 1 : pp. 38–61
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Sasaki-Ricci flow Sasaki-Ricci soliton transverse Fano Sasakian manifold transverse Sasaki-Futaki invariant transverse $K$-stable Foliation singularities.