×

CR-hypersurfaces of complex projective space. (English) Zbl 0815.53065

Let \(M\) be a compact, minimal, foliate, CR-real hypersurface of the \(n\)-dimensional complex projective space \(\mathbb{C} P^ n\) equipped with the Fubini-Study metric of constant holomorphic sectional curvature 4. If the square of the length of the second fundamental form of \(M\) is \(\leq 2n - 2\), then \(n = 1\) and \(M\) is totally geodesic in \(\mathbb{C} P^ 1\).
Reviewer: J.Berndt (Köln)

MSC:

53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
PDFBibTeX XMLCite
Full Text: DOI EuDML