In this manuscript, we study the Lorentz hypersurfaces of the Lorentz 5-pseudosphere (i.e. the pseudo-Euclidean 5-sphere) S_1^5 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_1^5. We present an affirmative answer to the extended conjecture on Lorentz hypersurfaces with three distinct principal curvatures.
