Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres
Let B be a submanifold of a Riemannian manifold (M,g), and \(\phi_ B\) the reflection with respect to B, reversing geodesics orthogonal to B on a sufficiently small tubular neighborhood. We derive a characterization of the property that \(\phi_ B\) is isometric by means of the Ricci operator on geodesic spheres tangent to B.
scientific article; zbMATH DE number 4171879