A basic inequality and new characterization of Whitney spheres in a complex space form
The authors consider an \(n\)-dimensional Lagrangian submanifold \(M\) of the \(n\)-dimensional complex space form of constant holomorphic sectional curvature. The authors derive an inequality involving \(| \overline{\nabla} h| ^2,\) where \(h\) is the second fundamental form, and \(| \nabla^\perp \vec{H}| ^2,\) where \(\vec{H}\) is the mean curvature vector, that is \[ | \overline{\nabla} h| ^2\geqslant \frac{3n^2}{n +2}| \nabla^\perp \vec{H}| ^2 \] They classify all submanifolds that realize at every point the equality, giving a a characterization of the Whitney spheres in a complex space form.
scientific article; zbMATH DE number 2174710