Force free projective motions of the sphere |
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Authors: | M Marcela Lazarte Marcos Salvai Adrián Will |
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Institution: | 1. FaMAF-CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina;2. Departamento de Matemática, FaCET, Av. Independencia 1800, 4000 Tucumán, Argentina |
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Abstract: | Suppose that the sphere Sn has initially a homogeneous distribution of mass and let G be the Lie group of orientation preserving projective diffeomorphisms of Sn. A projective motion of the sphere, that is, a smooth curve in G, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sn and, more generally, examples of subgroups H of G such that a force free motion initially tangent to H remains in H for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=SOn+1). The main tool is a Riemannian metric on G, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. |
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Keywords: | 22E43 22E70 53C22 70K25 |
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