Speaker: Professor Mo Xiaohuan
Topic: On Finsler gradient Ricci solitons
Date: September 6th, 2024 (Friday)
Time: 3.00 p.m.- 4.30 p.m.
Venue: Academic Lecture Hall 1506, Jingyuan Building
Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology
Biography:
Mo Xiaohuan is a professor at the School of Mathematical Sciences, Peking University. Professor Mo has been engaged in research and teaching in geometry for a long time. His main research focuses on Riemann-Finsler geometry and geometric calculus of variation. He has published 132 academic papers, more than 100 of which have been included in SCI, and his papers have been cited 787 times (MathSciNet).
Abstract:
In this lecture we discuss a class of Finsler measure space whose weighted Ricci curvature satisfies Ric_infty=cF^2. This class contains all gradient Ricci solitons and Finsler Gaussian solitons. Thus Finsler measure spaces in this class are called Finsler gradient Ricci solitons. For a Randers measure space, we find sufficient and necessary conditions for this space to be a Finsler gradient Ricci soliton. In particular, we show that Finsler gradient Ricci solitons must have isotropic S-curvature. Then we explicitly construct new infinitely many n-dimensional complete Finsler gradient Ricci solitons. In particular, we find an eigenfunction and its eigenvalue for such spaces generalizing the result previously only known for the case of Gaussian shrinking soliton. Finally we give necessary and sufficient conditions on the coordinate functions for these spaces to be Euclidean measure spaces.