Yano, Kentaro; Kon, Masahiro Conformally flat anti-invariant submanifolds of Sasakian space forms. (English) Zbl 0577.53034 Algebraic and differential topology - global differential geometry, Occas. 90th Anniv. M. Morse’s Birth, Teubner-Texte Math. 70, 334-342 (1984). [For the entire collection see Zbl 0568.00013.] Let \(\tilde M\) be a Sasakian manifold and M be a conformally flat anti- invariant submanifold of \(\tilde M,\) tangent to the structure vector field of \(\tilde M.\) Then the authors prove that M is locally a Riemannian product \(N\times R\), where N is a totally geodesic hypersurface of M of constant curvature. More results are obtained when \(\tilde M\) is a Sasakian space form. Reviewer: A.Bejancu Cited in 5 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C40 Global submanifolds Keywords:Sasakian manifold; conformally flat anti-invariant submanifold; Riemannian product Citations:Zbl 0568.00013 PDFBibTeX XML