Submanifolds of generalized Sasakian space forms
Recently the authors and \textit{D. E. Blair} introduced in [Isr. J. Math. 141, 157--183 (2004; Zbl 1064.53026)] the notion of a generalized Sasakian space form. In the present paper the submanifolds of such a space form are studied. It is focused on almost semi-invariant submanifolds, which were initiated by \textit{M. M. Tripathi} and \textit{K. D. Singh} [Demonstr. Math. 29, No. 2, 413--426 (1996; Zbl 0896.53041)], followed by \textit{M. M. Tripathi} and \textit{I. Mihai} [Note Mat. 20(2000--2001), No. 2, 135--164 (2001; Zbl 1097.53037)], and generalize invariant, anti-invariant, and slant submanifolds. Sectional curvatures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.
scientific article; zbMATH DE number 5605700