A characterization of hyperbolic spaces
Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1103-1107
https://doi.org/10.4134/BKMS.b170607
Published 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
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