Abstract
We prove that a substantial isometric immersion into a space form \(f:M^n\rightarrow \mathbb {Q}_c^{n+p}\) with negative extrinsic curvature and flat normal bundle whose first normal bundle has the lowest possible rank possesses substantial codimension \(p=n-1\). This fact is already known in the rather special case when also \(M^n\) has constant sectional curvature.
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MD, C-RO and ThV contributed equally to the above research. All authors read and approved the final manuscript.
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Dajczer, M., Onti, C.R. & Vlachos, T. The Codimension of Submanifolds with Negative Extrinsic Curvature. Results Math 78, 42 (2023). https://doi.org/10.1007/s00025-022-01818-x
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DOI: https://doi.org/10.1007/s00025-022-01818-x