A Geometric Approach to the Classification of the Equilibrium Shapes of Self-Gravitating Fluids |
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Authors: | Alvaro Pelayo Daniel Peralta-Salas |
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Institution: | (1) Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109-1043, USA;(2) Departamento de Física Teórica II, Universidad Complutense, 28040 Madrid, Spain |
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Abstract: | 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. |
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