On infinitesimal bendings of troughs of revolution. II

It is shown that if a trough of revolution $S\in C^1$ does not admit $C^1$ infinitesimal bendings with the parabolic parallel fixed, then $S$ possesses second-order $C^1$-rigidity, and the existence of first-order bendings is determined by a certain effectively verifiable necessary and sufficient condition on the meridian.
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