作者：Jian; Bo; FANG; Feng; Jiang; LI标量曲率超曲面常数自由曲面各向同性主曲率不变量变换群
摘要：Let x:M~(n-1)→R~n be an umbilical free hypersurface with non-zero principal curvatures.Two basic invariants of M under the Laguerre transformation group of R~n are Laguerre form C and Laguerre tensor L.In this paper,we prove the following theorem:Let M be an(n-1)-dimensional(n >3) complete hypersurface with vanishing Laguerre form and with constant Laguerre scalar curvature R in R~n,denote the trace-free Laguerre tensor by L =L-1/n-1tr(L)·Id.If sup_M ||L||=0,then M is Laguerre equivalent to a Laguerre isotropic hypersurface;and if sup_M ||L||=((n-1)(n-2))~(1/2)R/((n-1)(n-2)(n-3)),M is Laguerre equivalent to the hypersurface x:H~1×S~(n-2)→R~n.
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