A characterization of geodesic hyperspheres of quaternionic projective space (Q1375774)

Let \(M\) be a real hypersurface of a quaternionic projective space \(QP^m\), \(m\geq 3\). Denote by \(R\) the Riemannian curvature tensor and by \(A\) the shape operator of \(M\). The author proves that \(M\) is an open part of a geodesic hypersphere in \(QP^m\) if and only if \(R(X,Y) AZ+R(Y,Z) AX+R(Z,X) AY=0\) holds for all vector fields \(X,Y,Z\) tangent to the maximal quaternionic subbundle of the tangent bundle \(TM\) of \(M\).