论文标题
3个manifolds的曲率基因座
Curvature loci of 3-manifolds
论文作者
论文摘要
我们完善了四边形的真实网络的仿射分类，以便获得常规$ 3 $ -MANIFOLDS的通用曲率基因座，$ \ Mathbb {r}^6 $和Singular Corank $ 1 $ $ 3 $ -MANIFOLDS in $ \ MATHBB {R}^5 $。为此，我们通过4个三位立方体给出的方程系统的数量和解决方案的曲率基因座的类型（在某些情况下是决定性变化）。我们还研究了，当歧管正朝切线前投影时，常规3个manifold的曲率基因座的奇异性如何变为无穷大。
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.
