On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form
Let \(M\) be a compact hypersurface of some standard space \(\mathbb{K}^n (\lambda)\) of constant curvature \(\lambda\) lying in a ball \(B_R\subset \mathbb{K}^n(\lambda)\) of some radius \(R\). The authors give a characterization for \(M=\partial B_R\) in terms of two inequalities in which integrals over the Ricci and scalar curvature of \(M\) are involved. As essential tool they derive an integral formula which for \(\lambda=0\) reduces to the Minkowski formula.
hypersurfaces of spaces of constant curvature
scientific article; zbMATH DE number 902612
scientific article