The Kähler-Ricci flow on Kähler manifolds with 2-non-negative traceless bisectional curvature operator

Abstract

The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kähler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kähler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.

Keywords

Kähler-Ricci flow / 2-Non-negative bisectional curvature

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