Global rigidity theorems of hypersurfaces
which is the natural generalization of one of the following two conditions, (1) tr r (2) (tr r ]r =constant_>0. We also note that the condition (0.1) comes out naturally when we study the operatot []. Let M be an n-dimensional hypersurface in an (n+ 1)-dimensional real space form Rn+l(c). Observing that the second fundamental form tensor hij is a natural Codazzi tensor on M, in Section 2, we apply the study of Section 1 to these hypersurfaces and obtain general rigidity results (see Theorem 2.1 and Theorem 2.2) which unify some existing results. Condition (0.1) becomes in this case