Abstract
We analyze the existence of isometric immersions of submanifolds of space forms, preserving the second fundamental form, or a convenient projection of it, into totally geodesic submanifolds of lower dimensions. We characterize some normal fields (that we call Codazzi and Ricci fields) whose global existence ensures such an isometric reduction of the codimension. We relate the existence of these fields to the behaviour of the curvature locus at each point of the submanifold and analyze conditions for the existence of isometric immersions into spheres and the vanishing of the normal curvature.
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Schedule a callMore From: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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