A Note on Compact Kähler-ricci Flow with Positive Bisectional Curvature
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چکیده
We show that for any solution gij̄(t) to the Kähler-Ricci flow with positive bisectional curvature Rīijj̄(t) > 0 on a compact Kähler manifold M , the bisectional curvature has a uniform positive lower bound Rīijj̄(t) > C > 0. As a consequence, gij̄(t) converges exponentially fast in C ∞ to an KählerEinstein metric with positive bisectional curvature as t → ∞, provided we assume the Futaki-invariant of M is zero. This improves a result of D. Phong, J. Song, J. Sturm and B. Weinkove [20] in which they assumed the stronger condition that Mabuchi K-energy is bounded from below.
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تاریخ انتشار 2008