Geodesic
The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3)
Journal of Singularities, Tome 21 (2020), pp. 1-14

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We study the flat geometry of the least degenerate singularity of a singular surface in R^4, the I_1 singularity parametrised by (x,y)->(x,xy,y^2,y^3). This singularity appears generically when projecting a regular surface in R^5 orthogonally to R^4 along a tangent direction. We obtain a generic normal form for I_1 invariant under diffeomorphisms in the source and isometries in the target. We then consider the contact with hyperplanes by classifying submersions which preserve the image of I_1. The main tool is the study of the singularities of the height function.
DOI : 10.5427/jsing.2020.21a
Classification : 57R45, 53A05, 58K05 
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     journal = {Journal of Singularities},
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     volume = {21},
     year = {2020},
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The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3). Journal of Singularities, Tome 21 (2020), pp. 1-14. doi: 10.5427/jsing.2020.21a

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