Curvature loci of 3-manifolds

2022/04/26 by Pedro Benedini Riul, Riul, Pedro Benedini, María Aparecida Soares Ruas +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2204.12312

Abstract

We refine the affine classification of real nets of quadrics in order to obtain generic curvature loci of regular 3-manifolds in ℝ⁶ and singular corank 1 3-manifolds in ℝ⁵. 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.

Related

• Singular 3-manifolds in ℝ⁵
• Relating second order geometry of manifolds through projections and normal sections
• Critical Curvature of Algebraic Surfaces in Three-Space
• Three-manifolds with constant vector curvature
• Axial curvatures for corank 1 singular n-manifolds in \mathbb R^n+k