Determinantal variety and normal embedding
Algebraic Geometry
2017-02-28 v3 Differential Geometry
Abstract
The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bilipschitz equivalence for intrinsic and extrinsic metrics on GL^+_n, exploiting the conical structure of the stratification of the space of n by n matrices by rank.
Cite
@article{arxiv.1602.01227,
title = {Determinantal variety and normal embedding},
author = {Karin U. Katz and Mikhail G. Katz and Dmitry Kerner and Yevgeny Liokumovich},
journal= {arXiv preprint arXiv:1602.01227},
year = {2017}
}
Comments
8 pages. To appear in Journal of Topology and Analysis