Biharmonic hypersurfaces in the standard Lorentz ۵-pseudosphere

In this manuscript, we study the Lorentz hypersurfaces of the Lorentz ۵-pseudosphere (i.e. the pseudo-Euclidean ۵-sphere) S^۵_۱ having three distinct principal curvatures. A well-known conjecture of Bang-Yen Chen on Euclidean spaces says that every submanifold is minimal. We consider an advanced version of the conjecture on Lorentz hypersurfaces of S^۵_۱. We present an affirmative answer to the extended conjecture on Lorentz hypersurfaces with three distinct principal curvatures.

کلیدواژه ها:

C-biharmonic ، isoparametric ، de-Sitter space ، ۱-minimal