On Kähler manifolds with positive orthogonal bisectional curvature

الأصل · EN

In this paper, we study any Kähler manifold where the positive orthogonal bisectional curvature is preserved on the Kähler Ricci flow. Naturally, we always assume that the first Chern class C₁ is positive. In particular, we prove that any irreducible Kähler manifold with such property must be biholomorphic to CPⁿ. This can be viewed as a generalization of Siu-YauSiuy80, Morri's solution Mori79 of the Frankel conjecture. According to [8], note that any Kähler manifold with 2-positive traceless bisectional curvature operator is preserved under Kahler Ricci flow; which in turns implies the positivity of orthogonal bisectional curvature under the flow.