Einstein parallel Kaehler submanifolds in a complex projective space
A submanifold is said to be bi-order if the immersion is given by eigenfunctions of the Laplacian corresponding to two distinct eigenvalues. More precisely, a submanifold is said to be of order \(\{\) p,q\(\}\) if the immersion is given by the p-th and the q-th eigenfunctions. The author proves among others that the following conditions are mutually equivalent for a compact Kähler submanifold of a complex projective space: (1) Einstein parallel submanifold which is not totally geodesic, (2) bi-order, (3) of order \(\{\) 1,2\(\}\).
scientific article; zbMATH DE number 3992358