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甬江数学讲坛75讲(2020年第2讲)

发布日期:2020-01-10 作者:数学与统计学院 文章来源:未知  责任编辑:

人:莫小欢

报告时间:2020114 1000-1100

报告地点:龙赛理科楼116会议室

专家简介:莫小欢, 北京大学数学科学学院教授,博士生导师,长期从事几何学的教学和研究。2002年荣获教育部提名国家自然科学奖一等奖(独立),2007年主持的《几何学》课程被评为国家级精品课,2009年获得国家教学成果二等奖。先后应邀前往美国麻省理工大学,加州大学伯克利分校,德国马克思·普朗克数学研究所(波思与莱比锡),法国高等科学研究院,意大利国际理论物理中心,巴西巴西利亚大学和坎皮纳斯大学等世界著名科研机构访问。2002年来连续主持国家自然科学基金项目.目前已发表学术论文110余篇,其中被SCI收录90余篇,论文被引用达到527次。

 

报告题目-1Inverse problem of sprays with scalar curvature

报告摘要:Every Finsler metric on a differential manifold induces a spray. The converse is not true. Therefore it is one of the most fundamental problems in spray geometry to determine whether a spray is induced by a Finsler metric which is regular, but not necessary positive definite. This problem is called inverse problem. In this lecturewe discuss inverse problem of sprays with scalar curvature. In particular, we show that if such a spray $G$ on a manifold is of vanishing $H$-curvature, but $G$ has not isotropic curvature, then $G$ is not induced by any (not necessary positive definite) Finsler metric. We also find infinitely many sprays on an open domain $U\subset\mathbb{R}^n$ with scalar curvature and vanishing $H$-curvature, but these sprays have no isotropic curvature. This contrasts sharply with the situation in Finsler geometry.

 

报告题目-2Funk functions and constructions of dually flat Finsler metrics

报告摘要:Dually flat Finsler metrics arise from $\alpha$-flat information structures on Riemann-Finsler manifolds. Inspired by the theory of Funk functions and Hamel functions due to Li-Shen, we give a new approach to produce dually flat Finsler metrics in this lecture. Moreover, we manufacture new dually flat spherically symmetric Finsler metrics by using the standard Euclidean norm on $\mathbb{R}^n$. 

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