Work

$L^4$-Bound of the Transverse Ricci Curvature under the Sasaki-Ricci Flow

Year: 2025

Type: article

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.

Source: Journal of Mathematical Study

DOI: 10.4208/jms.v58n1.25.03

Authors: Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu

Institutions: National Taiwan University, Chongqing University of Technology, Xinyang Normal University, National Pingtung University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408991729

FWCI:

Cites: 62

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Related to: 10