In this talk, we classify timelike hypersurfaces in (n+1)-dimensional pseudo-sphere whose position map x: M_1^n \to S_1^{n+1} satisfies the condition B x=m x + c, where B is the well-known Cheng-Yau operator, m is a constant matrix and c is a constant vector. This condition is an extension of a well-known equation Delta x=m x+ c, where Delta is the well-known Laplace operator. As an extension of Takahashi's theorem, we show that such a hypersurface has to be 1-minimal or an open piece of S_1^n(c), S_1^m(c)\times R^{n-m} or S^m(c)\times L^{n-m} for some c>0 and 1
