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 A characterization of hyperbolic spaces Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1103-1107 https://doi.org/10.4134/BKMS.b170607Published online July 31, 2018 Dong-Soo Kim, Young Ho Kim, Jae Won Lee Chonnam National University, Kyungpook National University, Gyeongsang National University Abstract : Let $M$ be a complete spacelike hypersurface in the $(n+1)$-dimensional Minkowski space ${\mathbb L}^{n+1}$. Suppose that every unit speed curve $X(s)$ on $M$ satisfies $\\ge -1/r^2$ and there exists a point $p\in M$ such that for every unit speed geodesic $X(s)$ of $M$ through the point $p$, $\= -1/r^2$ holds. Then, we show that up to isometries of ${\mathbb L}^{n+1}$, $M$ is the hyperbolic space $H^n(r)$. Keywords : Minkowski space, hyperbolic space, normal curvature, spacelike hypersurface MSC numbers : 53B25, 53B30 Downloads: Full-text PDF