2023/02/16 by Gonçalo Oliveira, Oliveira, Goncalo
Mathematics · #53C22 #53C25 #53C26 #58E10 #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2302.08354
openalex publication_date 2023/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by some conjectures originating in the Physics literature, we use Foscolo's construction of Ricci-flat Kahler metrics on K3 surfaces to locate, with high precision, several closed geodesics and compute their index (their length is also approximately known). Interestingly, the construction of these geodesics is related to an open problem in electrostatics posed by Maxwell in 1873. Our construction is also of interest to modern Physicists working on (supersymmetric) non-linear sigma models with target space such a K3 surface.