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We prove that, in Minkowski space, if a spacelike, $(n-1)$-convexhypersurface $M$ with constant $\sigma_{n-1}$ curvature has bounded principalcurvatures, then $M$ is convex. Moreover, if $M$ is not strictly convex, afteran $\mathbb{R}^{n,1}$ rigid motion, $M$ splits as a product$M^{n-1}\times\mathbb{R}.$ We also construct nontrivial examples of strictlyconvex, spacelike hypersurface $M$ with constant $\sigma_{n-1}$ curvature andbounded principal curvatures.

Entire spacelike hypersurfaces with constant $\sigma_{n-1}$ curvature in Minkowski space