Biharmonic hypersurfaces in \(E^5\) with zero scalar curvature
In 1991, \textit{B. Y. Chen} conjectured that all biharmonic submanifolds of Euclidean spaces are minimal [Soochow J. Math. 17, No. 2, 169--188 (1991; Zbl 0749.53037)]. While this conjecture in its general form is still open, substantial progress has been made under additional assumptions and in special cases. This article belongs to this direction of research. Using techniques of \textit{Th. Hasanis} and \textit{Th. Vlachos} [Math. Nachr. 172, 145--169 (1995; Zbl 0839.53007)], the authors prove that all biharmonic hypersurfaces of zero scalar curvature in Euclidean space \(E^5\) are minimal.
scientific article; zbMATH DE number 6504476