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The Hamiltonian of the $N$-particle Calogero model can be expressed in termsof generators of a Lie algebra for a definite class of representations.Maintaining this Lie algebra, its representations, and the flatness of theRiemannian metric belonging to the second order differential operator, the setof all possible quadratic Lie algebra forms is investigated. For N=3 and N=4such forms are constructed explicitly and shown to correspond to exactlysolvable Sutherland models. The results can be carried over easily to all $N$.Comment: 23 pages, 2 figures, replaced and enlarged versio

EXACTLY SOLVABLE DYNAMICAL SYSTEMS IN THE NEIGHBORHOOD OF THE CALOGERO MODEL