In this talk I will discuss a characterization of weighted projective spaces by a positive curvature condition. This can be viewed as an extension of the Mori-Siu-Yau theorem on the Frankel conjecture. The proof involves geometric involution equation combined with a finite dimensional deformation in Sasaki geometry. The latter is an odd dimensional cousin of Kahler geometry, and is intimately related to the theory of affine cones with isolated singularities.