Abstract
Infinitesimal rigidity and shakiness of jointed rodworks or polyhedra have been of major interest in recent research in geometry. In this paper structures of this type are investigated in spheres and projective spaces. A transformation is given showing that essentially no new structures occur in these spaces compared with the euclidean case. The main tool is the projective invariance of shaky structures. Shaky structures in euclidean space can be obtained as affine sections of shaky structures in a projective space of the same dimension.
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Wegner, B. Wackelige Gelenkwerke und wackelige Polyeder in Der sphärischen Geometrie. J Geom 25, 39–48 (1985). https://doi.org/10.1007/BF01222944
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DOI: https://doi.org/10.1007/BF01222944