TY - JOUR
T1 - $L^4$-Bound of the Transverse Ricci Curvature under the Sasaki-Ricci Flow
AU - Chang , Shu-Cheng
AU - Han , Yingbo
AU - Lin , Chien
AU - Wu , Chin-Tung
JO - Journal of Mathematical Study
VL - 1
SP - 38
EP - 61
PY - 2025
DA - 2025/03
SN - 58
DO - http://doi.org/10.4208/jms.v58n1.25.03
UR - https://global-sci.org/intro/article_detail/jms/23937.html
KW - Sasaki-Ricci flow, Sasaki-Ricci soliton, transverse Fano Sasakian manifold, transverse Sasaki-Futaki invariant, transverse $K$-stable, Foliation singularities.
AB - <p style="text-align: justify;">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.</p>