Kim, Hyang Sook; Pyo, Yong-Soo On the Chern-type problem in a complex projective space. (English) Zbl 0961.53029 Balkan J. Geom. Appl. 4, No. 2, 69-81 (1999). 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. Reviewer: Neda Bokan (Beograd) MSC: 53C40 Global submanifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Kähler manifold; second fundamental form; complex submanifold; complex projective space PDFBibTeX XMLCite \textit{H. S. Kim} and \textit{Y.-S. Pyo}, Balkan J. Geom. Appl. 4, No. 2, 69--81 (1999; Zbl 0961.53029) Full Text: EuDML EMIS