English

Electrostatics and geodesics on $K3$ surfaces

Differential Geometry 2023-02-17 v1 Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.2302.08354,
  title  = {Electrostatics and geodesics on $K3$ surfaces},
  author = {Goncalo Oliveira},
  journal= {arXiv preprint arXiv:2302.08354},
  year   = {2023}
}

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R2 v1 2026-06-28T08:41:55.775Z