2009/04/22 by Bruce Solomon, Solomon, Bruce
Computer Science · Mathematics · #53A05 #53A15 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.0904.3493
openalex publication_date 2009/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A surface S in R3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete, connected C2 surface with cpo must be either a generalized cylinder, or quadric. Applying this, we deduce that a complete C2 surface containing a transverse plane oval but no skewloop, must be a cylinder or a quadric.