On real hypersurfaces of finite type of \(CP^ m\)
Let \(\psi\) : \({\mathbb{C}}P^ m\to H(m+1)\) be the standard embedding of \({\mathbb{C}}P^ m\) as the set of primitive idempotents. An isometric immersion \(i: M\to {\mathbb{C}}P^ m\) of a real Riemannian manifold is called k-order, if in the spectral decomposition of \(\psi\) \(\circ i\) with respect to the Laplacian only k eigenspaces belonging to positive eigenvalues are involved. The authors study such immersions of real codimension 1 and low k. They classify (closed) Mono-order \((k=1)\) and minimal Bi-order \((k=2)\) real hypersurfaces.
scientific article; zbMATH DE number 3901566