Taut submanifolds are algebraic
Differential Geometry
2014-10-21 v3
Abstract
We prove that every (compact) taut submanifold in Euclidean space is real algebraic, i.e., is a connected component of a real irreducible algebraic variety in the same ambient space. This answers affirmatively a question of Nicolaas Kuiper raised in the 1980s.
Cite
@article{arxiv.1102.1704,
title = {Taut submanifolds are algebraic},
author = {Quo-Shin Chi},
journal= {arXiv preprint arXiv:1102.1704},
year = {2014}
}
Comments
24 pages. The two previous versions carrying the same title are meshed in the current one, where the scheme follows the first version of the semialgebraic approach and is made precise by the unit tangent cones of focal sets introduced in the second version. A section on semialgebraic sets is included to review certain important properties, such as the slicing theorem, etc