Higher Schl{\"a}fli Formulas and Applications II. Vector-valued differential relations
微分几何
2009-01-20 v3 几何拓扑
摘要
The classical Schl\"afli formula, and its ``higher'' analogs given in [SS03], are relations between the variations of the volumes and ``curvatures'' of faces of different dimensions of a polyhedra (which can be Euclidean, spherical or hyperbolic) under a first-order deformation. We describe here analogs of those formulas which are vector-valued rather than scalar. Some consequences follow, for instance constraints on where cone singularities can appear when a constant curvature manifold is deformed among cone-manifolds.
关键词
引用
@article{arxiv.math/0611499,
title = {Higher Schl{\"a}fli Formulas and Applications II. Vector-valued differential relations},
author = {Jean-Marc Schlenker and Rabah Souam},
journal= {arXiv preprint arXiv:math/0611499},
year = {2009}
}
备注
26 pages, no figure. v2: added 2 refs, improved intro. v3: added section on low dim examples