Work

Continuity Equation of Transverse Kähler Metrics on Sasakian Manifolds

Year: 2024

Type: article

Abstract: We introduce the continuity equation of transverse Kähler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normalized) continuity equation converges smoothly to the unique η-Einstein metric in the basic Bott–Chern cohomological class of the initial transverse Kähler metric (resp. first basic Chern class). These results are the transverse version of the continuity equation of the Kähler metrics studied by La Nave and Tian, and also counterparts of the Sasaki–Ricci flow studied by Smoczyk, Wang, and Zhang.

Source: Mathematics

DOI: 10.3390/math12193132

Authors: Yushuang Fan, Tao Zheng

Institutions: China University of Geosciences (Beijing), Beijing Institute of Technology

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

OpenAlex ID: W4403191675

FWCI:

Cites: 68

Cited by:

Related to: 10