Second order parallel tensors on generalized Sasakian space forms and semi parallel hypersurfaces in Sasakian space forms (Q846750)

It is proved that in a generalized Sasakian space form \(M(f_1,f_2, f_3)\) with \(f_1\neq f_2\), a second-order parallel symmetric tensor \(B\) is a constant multiple of the associated positive definite metric tensor. It is also proved that there are no semi-parallel hypersurfaces in a Sasakian space form \(M^{2n+1}(c)\), when \(c\neq 1\) and \(n\geq 2\).