DEFORMATIONS OF THE VERONESE EMBEDDING AND FINSLER -SPHERES OF CONSTANT CURVATURE

Abstract We establish a one-to-one correspondence between, on the one hand, Finsler structures $2$ -sphere with constant curvature $1$ and all geodesics closed, other Weyl connections certain spindle orbifolds whose symmetric Ricci is positive definite are closed. As an application of our duality result, we show that suitable holomorphic deformations Veronese embedding $\mathbb {CP}(a_1,a_2)\rightarrow \mathbb {CP}(a_1,(a_1+a_2)/2,a_2)$ weighted projective spaces provide examples -spheres