×

On the Chern-type problem in a complex projective space. (English) Zbl 0961.53029

Let \(M\) be an \(n(\leq 3)\)-dimensional complete complex submanifold of a complex projective space \(\mathbb{C} P^{n+p}(c)\). The authors give an inequality that the totally real bisectional curvatures of \(M\) satisfy when \(M\) is congruent to a complex projective space \(\mathbb{C} P^n(c)\). Furthermore they study an inequality satisfied by the squared norm \(h_2\) of the second fundamental form that characterizes \(M\) to be totally geodesic.

MSC:

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