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.
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Craveiro de Carvalho, F.J., Wegner, B. Diametrical Submanifolds. Periodica Mathematica Hungarica 40, 1–11 (2000). https://doi.org/10.1023/A:1004889304231
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DOI: https://doi.org/10.1023/A:1004889304231