Abstract
Extending some previous results of Sierra and Tironi (J Pure Appl Algebra 209:361–369, 2007) and Beorchia and Sacchiero (J Pure Appl Algebra 213:1750–1755, 2009 ), we complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.
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