Elimination of definite fold II

Osamu Saeki

Published 2017-09-12Version 1

In this paper, we first give a detailed proof to the elimination theorem of definite folds for smooth maps of manifolds of dimension > 2 into the 2-sphere or into the real projective plane, as the proof given in our previous paper lacked some detailed explanations. We also give a new proof from a different viewpoint and also present various explicit examples. Furthermore, we prove the non-existence of singular Legendre fibrations on 3-manifolds, answering negatively to a question posed in our previous paper.