Higher Schl{ä}fli Formulas and Applications II. Vector-valued differential relations

Details Higher Schl{ä}fli Formulas and Applications II. Vector-valued differential relations Higher Schl{ä}fli Formulas and Applications II. Vector-valued differential relations

2006-11-16

arxiv.org/abs/math/0611499v3

Int. Math. Res. Not. IMRN 2008, Art. ID rnn 068, 44 pp.

Mathematics

Differential Geometry

26 pages, no figure. v2: added 2 refs, improved intro. v3: added section on low dim examples

Scientific paper

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.

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