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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 $\<X''(s), X''(s)\>\ge -1/r^2$ and there exists a point $p\in M$ such that for every unit speed geodesic $X(s)$ of $M$ through the point $p$, $\<X''(s), X''(s)\>= -1/r^2$ holds. Then, we show that up to isometries of ${\mathbb L}^{n+1}$, $M$ is the hyperbolic space $H^n(r)$.
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참고문헌 (3)
참고문헌 신청
J. Baek / 2003 / A characterization of the unit sphere / Amer. Math. Monthly 110(9):830~833
D.-S. Kim / 2014 / On standard imbeddings of hyperbolic spaces in the Minkowski space / C. R. Math. Acad. Sci. Paris 352(12):1033~1038
B. O'Neill / 1983 / Semi-Riemannian Geometry, Pure and Applied Mathematics, 103 / Academic Press, Inc.
D.-S. Kim / 2014 / On standard imbeddings of hyperbolic spaces in the Minkowski space / C. R. Math. Acad. Sci. Paris 352(12):1033~1038
B. O'Neill / 1983 / Semi-Riemannian Geometry, Pure and Applied Mathematics, 103 / Academic Press, Inc.
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