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In this paper, we show that a generalized Sasakian space form of dimensiongreater than three is either of constant sectional curvature; or a canalhypersurface in Euclidean or Minkowski spaces; or locally a certain type oftwisted product of a real line and a flat almost Hermitian manifold; or locallya wapred product of a real line and a generalized complex space form; or an$\alpha$-Sasakian space form; or it is of five dimension and admits an$\alpha$-Sasakian Einstein structure. In particular, a local classification forgeneralized Sasakian space forms of dimension greater than five is obtained. Alocal classification of Riemannian manifolds of quasi constant sectionalcurvature of dimension greater than three is also given in this paper.

Generalized Sasakian space forms and Riemannian manifolds of quasi constant sectional curvature