Pointed Wiedersehen metrics on exotic spheres and diffeomorphisms of \(S^6\) (Q5956152)

The author gives an explicit Riemannian metric on an exotic sphere \(\Sigma^7\) satisfying the condition that the cut loci of points \(p\) belonging to a certain embedded circle in \(\Sigma^7\) are single points. Such points \(p\) are called Wiedersehen points. The construction of the Riemannian metric is similar in spirit to the one given by \textit{J. Cheeger} and \textit{D. Gromoll} in [Ann. Math. (2) 96, 413-443 (1972; Zbl 0246.53049)].