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Geometric Analysis Seminar

The Curvature Operator of the Second Kind

Xiaolong Li

Location:  Zoom https://rutgers.zoom.us/j/96991424202?pwd=QWJPbnBZMzdHMm5rWkx6ekNPK0tzQT09
Date & time: Tuesday, 23 April 2024 at 2:50PM - 3:50PM

The Riemann curvature tensor naturally induces two kinds of curvature operators, the first kind acting on two-forms and the second kind acting on symmetric two-tensors. In this talk, I will give an introduction to the notion of the curvature operator of the second kind, present the proof of Nishikawa's conjecture on the classification of manifolds with positive or nonnegative curvature operators of the second kind, and also discuss some analogous results on Kahler manifolds. Along the way, I will mention some interesting questions and conjectures.