Journal of the
Korean Mathematical Society JKMS

Let $M$ be a properly immersed timelike hypersurface of $\overline {M}$. If $M$ is a diagonal type, $M$ satisfies the generic condition under the certain conditions of the eigenvalues of the shape operator. Moreover, applying them to Raychaudhuri equation, we can show that $M$ satisfies the generic condition. Thus, by these results, we establish the singularity theorem for $M$ in $\overline{M}$.

Keywords: timelike hypersurface, diagonal point, generic condition, singularity, Raychaudhuri equation, Lagrange tensor, expansion, timelike convergence condition, strong energy condition

MSC numbers: 53C50, 83C75