Abstract
We study 3-manifolds in \({\mathbb {R}}^5\) with corank 1 singularities. At the singular point we define the curvature locus using the first and second fundamental forms, which contains all the local second order geometrical information about the manifold. Also, we relate the geometry of these objects to the geometry of regular 3-manifolds in \({\mathbb {R}}^6\).
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Work of P. Benedini Riul supported by FAPESP Grant 2019/00194-6.Work of M. A. S. Ruas supported by CNPq Grant 305695/2019-3 and FAPESP Grant 2019/21181-0. Work of A. de J. Sacramento supported by CNPq Grant 150469/2017-9.
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Riul, P.B., Ruas, M.A.S. & Sacramento, A.d.J. Singular 3-manifolds in \({\mathbb {R}}^5\). RACSAM 116, 56 (2022). https://doi.org/10.1007/s13398-021-01198-x
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DOI: https://doi.org/10.1007/s13398-021-01198-x