A geometric approach to the classification of the equilibrium shapes of self-gravitating fluids
نویسندگان
چکیده
The classification of the equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in Mathematical Physics. In this paper it is proved that the equilibrium shapes are isoparametric submanifolds. Some geometric properties of them are also obtained, e.g. classification and existence for some Riemannian spaces and relationship with the isoperimetric problem and the group of isometries of the manifold. Our approach to the problem is geometrical and allows to study the equilibrium shapes on general Riemannian spaces.
منابع مشابه
A geometric approach to the equilibrium shapes of self-gravitating fluids
The classification of the possible equilibrium shapes that a selfgravitating fluid can take in a Riemannian manifold is a classical problem in mathematical physics. In this paper it is proved that the equilibrium shapes are isoparametric submanifolds. Some geometric properties of the equilibrium shapes are also obtained, specifically the relationship with the isoperimetric problem and the group...
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