报告题目:浙江工业大学2022几何线上会议

报告人：莫小欢，杨国俊，黄利兵，崔宁伟，周林峰，张攀，朱红梅

报告时间：2022年8月21日 上午 7：50-12：00，下午14:00-17:00

报告地点：线上腾讯会议： 701 778 139

报告1题目：Inverse problem in spray geometry

报告人：莫小欢（北京大学）

报告1摘要：In this lecture,we discuss inverse problem in spray geometry. First, we show that if a spray S with scalar curvature on a manifold is of vanishing H-curvature, but S has not isotropic curvature, then S is not induced by any (not necessary positive definite) Finsler metric. Secondly, we show that if a spray S on a manifold M is of non-diagonalizable Riemann curvature for some , then S is not induced by any Finsler metric. We find infinitely many sprays with non-diagonalizable Riemann curvature on a Lie group, these sprays are not induced by Finsler metrics. Thirdly we study left invariant sprays with non-vanishing spray vectors on Lie groups. We prove that if such a spray on a Lie group G satisfies that G is commutative or S is projectively flat,then S is not induced by any (not necessary positive definite) left invariant Finsler metric. Finally we construct an abundance of the left invariant sprays on Lie groups which satisfy the conditions and the conclusions in above result.

报告2题目：Sprays on Hamel-Funk Functions Model

报告人：杨国俊（四川大学）

报告2摘要：Hamel functions of a spray play an important role in the study of the projective metrizability of the concerned spray, and Funk functions are special Hamel functions. A Finsler metric is a special Hamel function of the spray induced by the metric itself and a Funk metric is a special Funk function of a Minkowski spray. In this paper, we study sprays on a Hamel or Funk function model. Firstly, we give some basic properties of a Hamel or Funk function of a spray and some curvature properties of a Hamel or Funk function in projective relations. We use the Funk metric to construct a family of sprays and obtain some of their curvature properties and their metrizability conditions. Secondly, we consider the existence of Funk functions on certain spray manifold. We prove that there exist local Funk functions on a R-flflat spray manifold, and on certain projectively flflat Berwald spray manifolds, we construct a multitude of nonzero Funk functions. Finally, we introduce a new class of sprays called Hamel or Funk sprays associated to given sprays and Hamel or Funk functions. We obtain some special properties of a Hamel or Funk spray of scalar curvature, especially on its metrizability and the special form of its Riemann curvature.

报告3题目：A note on Einstein Finsler manifolds

报告人：黄利兵（南开大学）

报告3摘要：This talk is based on the following papers: [Huang-Shen 2019],[Huang-Mo 2019], [Huang 2015] and [Huang 2011].  The motivations are Chern's conjecture on the existence of Finsler metrics of constant Ricci curvature and Ziller's conjecture on the finiteness of Einstein Riemannian metrics on certain homogeneous spaces. We give negative answers to both conjectures by restricting our attention to homogeneous Finsler geometry.

报告4题目：A class of critical surfaces in a Finsler space under the volume preserving variation

报告人：崔宁伟（西南交通大学）

报告4摘要：In this talk, I will introduce a quantity  to establish the Minkowski formula on the submanifolds in the general -manifolds, and study the volume preserving hypersurfaces in special Finsler spaces. In particular, letbe the  3-dimensional Randers sapce where  and 0<b<1 is a constant. We study the critical surfaces under the volume preserving variation in  under the Busemann-Hausdorff measure. We use the quantity  to characterize such surfaces which are called the constant mean curvature surfaces.  Similar to the  Delaunay's famous work, we give a complete classification of the cmc  surfaces rotating around the -axis in the 3-dimensional Randers space with the Busemann-Hausdorff measure, which reduces to the classical Delaunay's cmc surfaces in  when b=0. All the examples in this paper are the first explicit cmc surfaces in Finsler geometry.

报告5题目：The minimal surfaces in the Finsler space forms

报告人：周林峰（华东师范大学）

报告5摘要：Utilizing the mean curvature formula obtained by N. Cui and L. Zhou, we established the mean curvature formula of the surfaces in K=0 and K=-1 Finsler space forms. Several interesting results are proved from the formula.

报告6题目：Some topics on Yang-Mills equations

报告人：张攀 （安徽大学）

报告6摘要：In this talk, I will introduce our recent work on Yang-Mills equations. And this talk will be divided into two parts. In the first part, I will review some classical results on the Yang-Mills flow, and then introduce our results on the higher order Yang-Mills-Higgs flow. Under some suitable conditions, we show that the flow admit long-time behavior. In the second part, I will talk about the existence of Hermite-Yang-Mills metric on non-Kaehler manifold. The proof is a combination of continuity method and heat flow method. This talk is based on joint works with Hemanth Saratchandran, Chuanjing Zhang, Jiaogen Zhang and Xi Zhang.

报告7题目：On a class of Finsler gradient steady Ricci soliton

报告人：朱红梅（河南师范大学）

报告7摘要：We investigate a class of Finsler gradient steady Ricci soliton. For a Douglas (α,β) measure space (M,F,dV ), we prove that if it is a Finsler gradient steady Ricci soliton, then up to a scaling, it must be a Finsler gradient square Ricci soliton.

邀请人：李影