科研之友
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摘要
This paper gives a new characterization of geodesic spheres in the hyperbolic space in terms of a "weighted" higher order mean curvature. Precisely, we show that a compact hypersurface Sigma(n-1) embedded in H-n with VHk being constant for some k = 1, ..., n - 1 is a centered geodesic sphere. Here H-k is the k-th normalized mean curvature of Sigma induced from H-n and V = cosh r, where r is a hyperbolic distance to a fixed point in H-n. Moreover, this result can be generalized to a compact hypersurface Sigma embedded in H-n with the ratio V (H-k/H-j) = constant, 0 <= j < k <= n - 1 and H-j not vanishing on Sigma.
