Deformations of the Vernonese embedding and Finsler 2-Spheres of constant curvature

Lange, Christian und Mettler, Thomas (2022): Deformations of the Vernonese embedding and Finsler 2-Spheres of constant curvature. In: Journal of the Institute of Mathematics of Jussieu, Vol. 21, No. 6: pp. 2103-2134

Abstract

We establish a one-to-one correspondence between, on the one hand, Finsler structures on the 2 -sphere with constant curvature 1 and all geodesics closed, and on the other hand, Weyl connections on certain spindle orbifolds whose symmetric Ricci curvature is positive definite and whose geodesics are all closed. As an application of our duality result, we show that suitable holomorphic deformations of the Veronese embedding P(a1,a2)→CP(a1,(a1+a2)/2,a2) of weighted projective spaces provide examples of Finsler 2-spheres of constant curvature whose geodesics are all closed.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1474-7480
• Language: English