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BIT Has Made Achievements in the Study of a Class of Completely Nonlinear Equations on Sasaki Manifolds

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  Beijing Institute of Technology, Dec 17th, 2019: Currently, Zheng Tao, deputy researcher of School of Mathematics and Statistics of Beijing institute of technology (BIT), published an online research paper titled Transverse fully nonlinear equations on Sasakian manifolds and applications in mathematics top academic journals Advances in Mathematics. The paper discusses the solvability of a class of completely nonlinear equations on Sasaki manifolds. As geometric application, the Galabi-Yau type theorems of both cross-cut (strong) Gauduchon metric and cross-sectional equilibrium metric on Sasaki manifolds are proved. At the same time, the paper points out that this kind of completely nonlinear equations can also be solved on the compact fold-bed manifolds with the cross-cut Hermite metric with a complex codimension of n. The Calabi-Yau theorems of both cross-cut Hermite metric and cross-cut (strong) Gauduchon metric are discussed as geometric application in the paper.

  

  Sasaki manifold was introduced by Sasaki, a Japanese mathematician, in the 1960s. It is the odd-dimensional counterpart of Kahler manifold and lies at the intersection of tangent-contacting manifold, Cauchy-Riemann manifold and Riemann manifold. In recent years, due to its important role in Riemann geometry, algebraic geometry and physics (such as Ads/CFT correspondence, string theory, etc.), Sasaki manifold has attracted more and more attention from mathematical and physical workers. Qiu Chengtong, Futaki and many other famous mathematicians have gained a large number of achievements on Sasaki manifold. Many famous conclusions on Kahler manifolds, including the Calabi-Yau theorem, Frankel conjecture, Kobayashi-Hitchin correspondence, k-stability, etc., have correspondence on Sasaki manifolds.

  

  Zheng Tao, an associate researcher, was inspired by Tosatti and Weinkove (j. Amer. Math. Soc.2010,2017) 's solvability of Monge-Ampere equations on Hermite manifolds and by Székelyhidi, Tosatti and Weinkove (Acta Math.2017)'s proof of the Gauduchon conjecture on Hermite manifolds, and thus conducted further studies to achieve this result.

  

  The work was carried out by BIT associate researcher Zheng Tao and postdoctoral researcher Feng Ke of the School of Mathematical Sciences, Peking University. The corresponding author is Zheng Tao.

  

Paper link address:

  https://www.sciencedirect.com/science/article/pii/S0001870819304475?via=ihub

  

Attached personal profile:

  Zheng Tao, associate researcher, member of the geometry team, School of Mathematics and Statistics, BIT. He received his bachelor's degree in Shandong University and his doctor's degree from the Institute of Mathematics and System Sciences, Chinese Academy of Sciences. Zheng Tao has been engaged in the research of complex differential geometry and related issues for a long time. He has been in charge of the General Program of Postdoctoral Fund, Special Support of Postdoctoral Fund and Youth Program of National Natural Science Foundation of China. As a corresponding author, he has published more than 10 SCI papers in top journals such as Advances in Mathematics and International Mathematics Research Notices.

  

News Source: School of Mathematics and Statistics

Editor: News Agency of BIT

Translation: News of Agency of BIT, Miao Yufei

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