Kim, Un Kyu Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms. (English) Zbl 1118.53025 Note Mat. 26, No. 1, 55-67 (2006). P. Alegre, D. E. Blair and A. Carriazo [Isr. J. Math. 141, 157–183 (2004; Zbl 1064.53026)] introduced the so-called generalized Sasakian-space forms. Such spaces are almost contact metric manifolds whose curvature tensor has a special expression. In the present paper, the author classifies generalized Sasakian-space forms under the additional assumption that they are conformally flat and the characteristic vector field is Killing. Moreover, he classifies locally symmetric generalized Sasakian-space forms. Reviewer: D. Perrone (Lecce) Cited in 29 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D15 Almost contact and almost symplectic manifolds Keywords:Generalized Sasakian-space-form; Conformally flat; Locally symmetric; Codazzi tensor; Almost contact metric manifold Citations:Zbl 1064.53026 PDFBibTeX XMLCite \textit{U. K. Kim}, Note Mat. 26, No. 1, 55--67 (2006; Zbl 1118.53025)