Continuity Equation of Transverse Kähler Metrics on Sasakian Manifolds

Yushuang Fan and Tao Zheng ()
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Yushuang Fan: Mathematical College, China University of Geosciences (Beijing), Beijing 100083, China
Tao Zheng: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2024, vol. 12, issue 19, 1-28

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.

Keywords: Sasakian manifold; basic Chern class; continuity equation; transverse Kähler metric; ? -Einstein metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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