$U(n)$-invariant Kähler metrics with nonnegative quadratic bisectional curvature

un 2 00 6 On Kähler manifolds with positive orthogonal bisectional curvature

The famous Frankel conjecture asserts that any compact Kähler manifold with positive bisectional curvature must be biholomorphic to CP n. This conjecture was settled affirmatively in early 1980s by two groups of mathematicians independently: Siu-Yau[16] via differential geometry method and Morri [15] by algebraic method. There are many interesting papers following this celebrated work; in parti...

Invariant Metrics with Nonnegative Curvature on Compact Lie Groups

We classify the left-invariant metrics with nonnegative sectional curvature on SO(3) and U(2).

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

Invariant Metrics with Nonnegative Curvature on So(4) and Other Lie Groups

We develop techniques for classifying the nonnegatively curved left-invariant metrics on a compact Lie group G. We prove rigidity theorems for general G and a partial classification for G = SO(4). Our approach is to reduce the general question to an infinitesimal version; namely, to classify the directions one can move away from a fixed bi-invariant metric such that curvature variation formulas...

On the Complex Structure of Kähler Manifolds with Nonnegative Curvature

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space C . We also show that the volume growth condition can be removed if ...