Metrics with conic singularities and spherical polygons
نویسندگان
چکیده
A spherical n-gon is a bordered surface homeomorphic to a closed disk, with n distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these polygons and enumerate them in the case that two angles at the corners are not multiples of π. The problem is equivalent to classification of some second order linear differential equations with regular singularities, with real parameters and unitary monodromy. MSC 2010: 30C20, 34M03.
منابع مشابه
On metrics of curvature 1 with four conic singularities on tori and on the sphere
We discuss conformal metrics of curvature 1 on tori and on the sphere, with four conic singularities whose angles are multiples of π/2. Besides some general results we study in detail the family of such symmetric metrics on the sphere, with angles (π/2, 3π/2, π/2, 3π/2). MSC 2010: 34M03, 34M05, 30C20, 35J91, 33E05.
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