Abstract
The study of isometric immersions becomes increasingly difficult for higher values of the codimension. Therefore, it is important to investigate whether the codimension of an isometric immersion into a space of constant sectional curvature can be reduced. That an isometric immersion \(f\colon M^n\to \mathbb {Q}_c^{n+p}\) admits a reduction of codimension to q < p means that there exists a totally geodesic submanifold \(\mathbb {Q}_c^{n+q}\) in \(\mathbb {Q}_c^{n+p}\) such that \(f(M)\subset \mathbb {Q}_c^{n+q}\). The possibility of reducing the codimension fits into the fundamental problem of determining the least possible codimension of an isometric immersion of a given Riemannian manifold into a space of constant sectional curvature.
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Dajczer, M., Tojeiro, R. (2019). Reduction of Codimension. In: Submanifold Theory . Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9644-5_2
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