Generalized Sasakian space forms were introduced by P. Alegre et al. [Isr. J. Math. 141, 157–183 (2004; Zbl 1064.53026)] as a natural generalization of Sasakian space forms, by replacing the constants appearing in the writing of their Riemann curvature tensors by differentiable functions.
In this paper, the author studies \(\phi \)-\(m\)-projectively flat, \(m\)-projectively flat, \(m\)-projectively locally symmetric and \(m\)-projectively locally \(\phi \)-symmetric generalized Sasakian space forms. He proves that any of these conditions is fulfilled if and only if the generalized Sasakian space form is conformally flat. He also offers two examples of this kind of manifolds. The reviewer remarks that there is a misprint in Example 5.2: obviously, \(f_1=1\).