Abstract
(1.1) Let c be a real number. Represent by A4"(c) a n-dimensional space form of curvature c. Let M N be a N-dimensional connected Riemannian manifold. The question that served as the starting point for this paper was to find simple conditions on the metric of M so that, if f:M"~ffl"+P(c), p>= 1, is an isometric minimal immersion then f is rigid in the following sense: given another minimal immersion g: M" ~ A4" + q(c), q >= p, then there exists a rigid motion T of M~ + q(c) such that g = To f, (~l"+P(c) being considered as a totally geodesic submanifold of
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