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Einstein Finsler Metrics and S. S. Chern's Question

2018/05/10 14:26  点击:[]

报告人: 程新跃 (重庆师范大学)

 

 : 2018年5月13日上午   9:30---10:30

 

 : 理科楼 LA107

 

 :The topic of this talk is driven by two motivations. The first motivation is from S. S. Chern’s question, i.e., whether or not every smooth manifold admits an Einstein Finsler metric with Ricci-constant. We use a Killing form with non-zero constant length on a Riemannian manifold to construct a family of (α, β)-metrics and we find equations that characterize Einstein metrics among this family of (α, β)-metrics. The constructed Einstein (α, β)-metrics may be Einstein Randers metrics or Ricci-flat (α, β)-metrics of Randers type with singularity, or Einstein almost regular (α, β)-metrics. The second motivation is from the following question: is there any Einstein-Finsler metric which is not of isotropic flag curvature on three dimensional manifolds? We have found Einstein (α, β)-metrics on S3 with Ric = 2F, Ric = 0 and Ric = −2F, respectively, but none of them are of constant flag curvature. Our results answer partly S. S. Chern’s question.

 

报告人简介: 程新跃,教授,博士生导师,重庆市学术技术带头人,重庆师范大学数学科学学院教授,上海大学博士生导师,西南大学兼职教授、博士生导师。历任重庆理工大学基础科学系副主任、数理学院院长、数学与统计学院院长、重庆市数学会副理事长。作为项目负责人获重庆市自然科学奖二等奖一项。论文发表在包括Journal of London Mathematical SocietyIsrael Journal of MathematicsAnnals of Global Analysis and Geometry在内的国际重要学术刊物上发表论文70余篇;与著名美籍华人数学家沈忠民合著的学术专著Finsler Geometry-- An Approach via Randers Spaces 由德国Springer出版社与科学出版社联合出版。

 

学院联系人: 朱长荣

 

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