Article,
On a special case of Connelly's suspension theorem.
Ryukyu Math. J., (1991)
Abstract
The author's introduction: ``Motivated by Cauchy's rigidity theorem
for convex polyhedra, R. Connelly investigated in J. Differ.
Geom. 13, 399-408 (1978; Zbl. 414.51013) the continuous rigidity
of suspensions of closed polygonal curves in 3-space. Suppose that
a suspension of a closed polygonal curve flexes in such a way that
the distance between the suspension points changes. Then, he proved
that the winding number of the closed curve about the line through
the suspension points is zero (when defined), and that the generalized
volume of the suspension equals zero. The proof of this result is
rather involved and difficult.Here, we consider closed polygonal
curves that are inscribed in a circle. For those curves, we can present
a simple and shorter proof of Connelly's suspension theorem, and
can characterize those polygonal curves whose suspensions are flexible.''.
