Shrinking solitons上Ricci曲率的非负性

On the non-negativity of the Ricci curvature on shrinking solitons

曲率的非负性是刻画流形的一个关键条件。证明了具有拼挤Weyl曲率的闭shrinking solitons上Ricci曲率一定是非负的。如果进一步假设Ricci曲率是正的,那么soliton是平凡的,即是Einstein流形。

The non-negativity of curved is a key condition to characterize Riemannian manifolds.It is shown that any closed shrinking solitons with pinched Weyl curvature must have non-negative Ricci curvature.If further assume the soliton has positive Ricci curvature,then it must be trivial,that is,the solition is an Einstein manifold.