Projections of transnormal manifolds (Q1114943)

This is an extension of research done by F. J. Craveiro de Carvalho [Port. Math. 45, No.4, 347-349 (1988; Zbl 0664.53027)]. Here it is shown that transnormality is not preserved under orthogonal projection onto hyperplanes without assuming that the manifold has the topological type of a sphere. This implies another general version of the transnormal graph theorem. Furthermore, in the case of closed transnormal curves in 3-space also non-orthogonal parallel projection onto planes is seen to destroy transnormality.