Abstract
Main Theorem. Suppose that M is a compact connected smooth manifold of di mension at least four. Then (1) For a generic choice of Riemannian metric on M, every prime minimal two-sphere f : S2 ?? M is free of branch points and lies on a nondegenerate critical submanifold of dimension six which is an orbit for the G-action, whereG = PSL(2,C). (2) For a generic choice of Riemannian metric on M, every prime minimal two-torus f : T2 ?> M is free of branch points and lies on a nondegenerate critical submanifold of dimension two which is an orbit for the G-action, whereG = S1 xS1. (3) For a generic choice of Riemannian metric on M, every prime oriented minimal surface f : S ? M of genus at least two is free of branch points and is Morse nondegenerate in the usual sense.
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