Mathematics – Differential Geometry
Scientific paper
2005-03-28
Mathematics
Differential Geometry
19 pages
Scientific paper
It was proved by H. Chen earlier that the property of the sum of any two eigenvalues of the curvature operator is positive is preserved under the ricci flow in all dimensional. By a recent result of Phong-Sturm, a similar notion of positive 2-traceless bisectional curvature positive is preserved on complex surface. We prove that this holds in all dimensional K\"ahler manifold. Moreover, the scalar curvature controls full curvature for this type of metrics.
Chen Xingming
Li Handong
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