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PreprintarXiv licencearXiv

Some remarks on robust features of surfaces in 4-space

  • Jorge Luiz Deolindo-Silva
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Abstract

We study robust features of smooth surfaces in 4-space associated with contact with lines and hyperplanes. We investigate the local and multi-local singularities of orthogonal projections and height functions that describe these contacts and their corresponding geometric loci on the surface. At an A4-singularity of a height function, we show that the A3-curve and the A1A2-curve are generically tangent with contact of order $2$. We further establish criteria for the versality of the families of height functions and orthogonal projections in terms of the regularity of the B2-curve and S2-curve, respectively. Finally, we obtain the [A2]- and (A0S0)2-curves arising from multi-local singularities of orthogonal projections and describe their tangency properties at the B3- and H3-singularities.

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Cite

BibTeXRIS
BibTeX
@misc{deolindosilva2026some,
  title = {{Some remarks on robust features of surfaces in 4-space}},
  author = {Jorge Luiz Deolindo-Silva},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40604},
  eprint = {2610.40604},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40604},
}
RIS
TY  - UNPB
TI  - Some remarks on robust features of surfaces in 4-space
AU  - Jorge Luiz Deolindo-Silva
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40604
UR  - https://arxiv.org/abs/2610.40604
AB  - We study robust features of smooth surfaces in 4-space associated with contact with lines and hyperplanes. We investigate the local and multi-local singularities of orthogonal projections and height functions that describe these contacts and their corresponding geometric loci on the surface. At an A_4-singularity of a height function, we show that the A_3-curve and the A_1A_2-curve are generically tangent with contact of order $2$. We further establish criteria for the versality of the families of height functions and orthogonal projections in terms of the regularity of the B_2-curve and S_2-curve, respectively. Finally, we obtain the [A_2]- and (A_0S_0)_2-curves arising from multi-local singularities of orthogonal projections and describe their tangency properties at the B_3- and H_3-singularities.
ER  -