Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}
Differential Geometry
2007-05-23 v1
Abstract
The projection of a compact oriented submanifold M^{n-1} in R^{n+1} on a hyperplane P^{n} can fail to bound any region in P. We call this ``projecting to zero.'' Example: The equatorial S^1 in S^2 projects to zero in any plane containing the x_3-axis. Using currents to make this precise, we show: A lipschitz (homology) (n-1)-sphere embedded in a compact, strictly convex hypersurface cannot project to zero on n+1 linearly independent hyperplanes in R^{n+1}. We also show, using examples, that all the hypotheses in this statement are sharp.
Keywords
Cite
@article{arxiv.math/0209226,
title = {Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}},
author = {Bruce Solomon},
journal= {arXiv preprint arXiv:math/0209226},
year = {2007}
}
Comments
14 pages, 4 figures