Abstract
The parabolic subset of a 3-manifold generically immersed in \(\mathbb {R}^4\) is a surface. We analyze in this study the generic geometrical behavior of such surface, considered as a submanifold of \(\mathbb {R}^4\). Typical Singularity Theory techniques based on the analysis of the family of height functions are applied in order to describe the geometrical characterizations of different singularity types.
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The authors would like to thank the referees for useful suggestions.
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A. C. Nabarro: Supported by FAPESP Grant 2016/19139-7.
C. Zanardo: Supported by CAPES Grant CSF-PVE-S 88887.122686/2016-00.
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Nabarro, A.C., Romero Fuster, M.C. & Zanardo, M.C. Geometry of the parabolic subset of generically immersed 3-manifolds in \(\mathbb {R}^4\). Res Math Sci 11, 42 (2024). https://doi.org/10.1007/s40687-024-00450-1
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DOI: https://doi.org/10.1007/s40687-024-00450-1
Keywords
- Parabolic surface of 3-manifolds in \(\mathbb {R}^4\)
- Height functions
- Geometrical characterizations for local singularities