题目：Weitzenbock formula and rigidity of canonical metrics on four-manifolds

报告人：吴鹏

地点：信息楼343研讨室

时间：2015年12月30日（周三）上午11:00-12:00

摘要： The Weitzenbock formula and curvature decompositions play the key role in the classification of Einstein four-manifolds with positive curvature. In this talk we will provide a new proof of the Weitzenbock formula for Einstein metrics using Berger curvature decomposition, and establish a unified framework for the Weitzenbock formula for a large class of canonical metrics on four-manifolds, which are called generalized m-quasi-Einstein metrics (or "Einstein metrics" on smooth metric measure spaces, including gradient Ricci solitons, quasi-Einstein metrics, and conformally Einstein metrics). As applications we will discuss several rigidity results for four-dimensional Einstein manifolds, conformally Einstein manifolds, gradient shrinking Ricci solitons, and quasi-Einstein manifolds.

简介：吴鹏本科和硕士毕业于北京大学，博士毕业于University of California, Santa Barbara分校，Cornell University助理教授（博士后）。研究方向为微分几何，目前的研究项目为四维流形上典则度量（即四维光滑度量测度空间上爱因斯坦度量）的刚性和光滑度量测度空间上的几何和分析。

吴鹏简历.pdf