COMPLETE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE AND CONSTANT MEAN CURVATURE IN R~4

Let M be a 3-dimersional complete and connected hypersurface immersed in R~4. If thescalar curvature R and the mean curvature |H| of M are constants, where |H|≠0, R≥0,then there are only three cases: R=6|H|~2, 9/2|H|~2 and 0. Moreovon we can find somehypersurfaces appropriate to these cases.

Complete Hypersurfaces with Constant Scalar Curvature and Constant Mean Curvature in R^4

Let M be a 3-dimersionaI complete and connected hyperscrface immersed in R^4. If the scalar curvature R and the mean curvature |H| of M are constants, where |H|\ne0,R\geq 0, then there are only three cases: R=6|H|^2,\frac{9}{2}|H|^2 and 0. Moreoven we can find some hypersurfaces appropriate to these cases.