Submanifolds of generalized Sasakian space forms. (English) Zbl 1176.53047

Recently the authors and 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 M. M. Tripathi and K. D. Singh [Demonstr. Math. 29, No. 2, 413–426 (1996; Zbl 0896.53041)], followed by M. M. Tripathi and 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.


53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C40 Global submanifolds
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