Curvature loci of 3‐manifolds

Pedro Benedini Riul, Raúl Oset Sinha and Maria Aparecida Soares Ruas

Mathematische Nachrichten, 2023, vol. 296, issue 10, 4656-4672

Abstract: We refine the affine classification of real nets of quadrics in order to obtain generic curvature loci of regular 3‐manifolds in R6$\mathbb {R}^6$ and singular corank one 3‐manifolds in R5$\mathbb {R}^5$. For this, we characterize the type of the curvature locus by the number and type of solutions of a system of equations given by four ternary cubics (which is a determinantal variety in some cases). We also study how singularities of the curvature locus of a regular 3‐manifold can go to infinity when the manifold is projected orthogonally in a tangent direction.

Date: 2023
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https://doi.org/10.1002/mana.202200170

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