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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

MSC:

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

Citations:

Zbl 0568.00013