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arXiv · 2204.12312

Curvature loci of 3-manifolds

Pedro Benedini Riul·Maria Aparecida Soares Ruas·Raúl Oset Sinha
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Abstract

We refine the affine classification of real nets of quadrics in order to obtain generic curvature loci of regular $3$-manifolds in $\mathbb{R}^6$ and singular corank $1$ $3$-manifolds in $\mathbb{R}^5$. For this, we characterize the type of the curvature locus by the number and type of solutions of a system of equations given by 4 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.

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Pedro Benedini Riul, Maria Aparecida Soares Ruas, Raúl Oset Sinha. 2022-04-26. Curvature loci of 3-manifolds. https://arxiv.org/abs/2204.12312

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