Diametrical submanifolds (Q5932647)

A diffeomorphism \(\delta:M\to M\) of a boundaryless \(k\)-dimensional submanifold \(M\) of a Euclidean space \(\mathbb{R}^n\) is called by the authors diametrical with respect to the center \(p\) if \(x\), \(p\) and \(\delta(x)\) \((x\in M)\) are distinct collinear points and \(T_x M=T_{\delta(x)} M\). Properties of such submanifolds, relations between \(M\) and its centers, consequences of the transnormality and of the equichordality of \(M\) etc. are studied. Several non-obvious examples are obtained.