JournalsrmiVol. 31, No. 1pp. 33–50

Projections of surfaces in R4\mathbb R^4 to R3\mathbb R^3 and the geometry of their singular images

  • Raúl Oset Sinha

    Universitat de València, Burjassot (Valencia), Spain
  • Farid Tari

    Universidade de São Paulo, São Carlos, Brazil
Projections of surfaces in $\mathbb R^4$ to $\mathbb R^3$ and the geometry of their singular images cover
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Abstract

We study the geometry of germs of singular surfaces in R3\mathbb R^3 whose parametrisations have an A\mathcal A-singularity of Ae\mathcal A_e-codimension less than or equal to 3, via their contact with planes. These singular surfaces occur as projections of smooth surfaces in R4\mathbb R^4 to R3\mathbb R^3. We recover some aspects of the extrinsic geometry of these surfaces in R4\mathbb R^4 from those of the images of their projections.

Cite this article

Raúl Oset Sinha, Farid Tari, Projections of surfaces in R4\mathbb R^4 to R3\mathbb R^3 and the geometry of their singular images. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 33–50

DOI 10.4171/RMI/825