BIRS Workshop Lecture Videos
Ivory's and Arnold's theorems on the sphere and in the hyperbolic space Izmestiev, Ivan
Take a solid shell bounded by two homothetic ellipsoids. Ivory's theorem says that the gravity inside the shell is zero; besides, if the shell is infinitely thin, the equipotential surfaces outside of it are confocal ellipsoids. Arnold's theorem generalizes the first part of the Ivory theorem (zero gravity) to certain algebraic surfaces. In this talk we present analogs of both theorems in the spherical and the hyperbolic space. This is a part of a joint work with Sergei Tabachnikov.
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