| Abstract: | A submanifold M of a Euclidean space is called diametrical with respect to a centre p if it admits a tangent preserving diffeomorphism such that the chords connecting the points on M with their images pass through p. Characterisations are given for the obvious situation, when M is reflectionally symmetric with respect to p and when M is spherical in addition to this. Moreover, non-obvious examples are obtained and the structure of diametrical submanifolds is investigated in more general cases. |
