报告题目：Gauss-Bonnet theorems in three-dimensional Riemannian Lie groups

主讲人：刘海明副教授（牡丹江师范大学）

报告邀请人：王咏乔副教授

报告时间：2021年12月29日下午15:00-16:30

报告地点：腾讯会议743-556-514

会议链接：https://meeting.tencent.com/dm/MdHLlwnwL1eV

报告摘要：Gauss-Bonnet theorem connects the intrinsic differential geometry of a surface with its topology and has many applications in physics and mathematics. In 2017, Z. Balogh, J. Tysonand E. Vecchiused a Riemannian approximation scheme to prove a Heisenberg version of the Gauss-Bonnet theorem(Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group.Mathematische Zeitschrift, vol. 287, pp.1-38, 2017.).They proposed an interesting question to understand to what extent similar phenomena hold in other sub-Riemannian geometric structures.Professor Wang, Dr. Wei and Dr. Wu investigated sub-Riemannian geometries of some typical spaces such as the affine group, the group of rigid motions of the Minkowski plane, the BCV spaces and the Lorentzian Heisenberg group, and proved Gauss-Bonnet theorems in these Lie groups. In this talk, we plan tointroduce some results on Gauss-Bonnet theorems in three-dimensional Riemannian Lie groups such as roto-translation group and the group of rigid motions of Minkowski plane with general left-invariant metric.

个人简历：刘海明，男，2015年6月毕业于东北师范大学基础数学专业，获理学博士学位，现任牡丹江师范学院数学科学学院副教授，硕士研究生导师，基础数学二级学科带头人，首批黑龙江省普通本科高校青年创新人才。研究方向为奇点理论、微分几何，现主持中央财政支持地方高校发展资金优秀青年人才项目，黑龙江省自然科学基金等项目，代表性成果发表在《中国科学：数学》，《Journal of Geometry and Physics》等期刊。