Biconservative Lorentz Hypersurfaces with at Least Three Principal Curvatures

Biconservative submanifolds, with important role in mathematical physics and differential geometry, arise as the conservative stress-energy tensor associated to variational problem of biharmonic submanifolds. Many examples biconservative hypersurfaces have constant mean curvature. A famous conjecture Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null Inspired by conjecture, we study Lorentz submanifolds Minkowski spaces. Although not been generally confirmed, it proven many cases, this led its spread various types submenifolds. As an extension, consider a advanced version (namely, $L_1$-conjecture) pseudo-Euclidean space $\mathbb{M}^5 :=\mathbb{E}^5_1$ (i.e. 5-space). We show every $L_1$-biconservative hypersurface $\mathbb{M}^5$ curvature at least three principal curvatures second