Surfaces with central cross-sections
Differential Geometry
2009-04-23 v2
Abstract
A surface S in R^3 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 C^2 surface with cpo must be either a generalized cylinder, or quadric. Applying this, we deduce that a complete C^2 surface containing a transverse plane oval but no skewloop, must be a cylinder or a quadric.
Cite
@article{arxiv.0904.3493,
title = {Surfaces with central cross-sections},
author = {Bruce Solomon},
journal= {arXiv preprint arXiv:0904.3493},
year = {2009}
}
Comments
35 pages, 3 figures