A note on biharmonic submanifolds of product spaces
Biharmonic submanifolds of a Riemannian manifold are those for which the inclusion map is biharmonic. For submanifolds in a product of two space forms, the author describes biharmonicity by two geometric differential equations. They are equations for the mean curvature vector and involve operators derived from a natural involution \(F\) associated with the product structure. There are a few geometric corollaries under the assumption that \(FH\) is tangent to the submanifold, or at least not normal. All of them state that there are either no biharmonic submanifolds or they are strongly restricted, if \(FH\) is tangent and additional assumptions hold.
scientific article; zbMATH DE number 6220945