Frankel conjecture

In the mathematical fields of differential geometry and algebraic geometry, the Frankel conjecture was a problem posed by Theodore Frankel in 1961. It was resolved in 1979 by Shigefumi Mori, and by Yum-Tong Siu and Shing-Tung Yau.
In its differential-geometric formulation, as proved by both Mori and by Siu and Yau, the result states that if a closed Kähler manifold has positive bisectional curvature, then it must be biholomorphic to complex projective space. In this way, it can be viewed as an analogue of the sphere theorem in Riemannian geometry, which (in a weak form) states that if a closed and simply-connected Riemannian manifold has positive curvature operator, then it must be diffeomorphic to a sphere. This formulation was extended by Ngaiming Mok to the following statement:
In its algebro-geometric formulation, as proved by Mori but not by Siu and Yau, the result states that if is an irreducible and nonsingular projective variety, defined over an algebraically closed field , which has ample tangent bundle, then must be isomorphic to the projective space defined over . This version is known as the Hartshorne conjecture, after Robin Hartshorne.