Ideal Einstein, conformally flat and semi-symmetric immersions
Let \(M\) be an ideal submanifold of a real space form, that is the invariants introduced in [\textit{B. Y. Chen}, Arch. Math. 60, 568--578 (1993; Zbl 0811.53060); Math. Proc. Camb. Philos. Soc. 128, 511--533 (2000; Zbl 0980.53096)] satisfy a certain equality. When \(M\) is either Einstein or conformally flat, then under sufficient conditions given here, \(M\) is totally geodesic. The paper ends with a complete classification of all ideal semi-symmetric hypersurfaces in real space forms.
scientific article; zbMATH DE number 1874394