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We examine symplectic topological features of certain family of monotoneLagrangian submanifolds in CP^n. Firstly, we give a cohomological restrictionfor Lagrangian submanifolds in CP^n whose first integral homologies are3-torsion. In particular, in the case where n=5,8, we prove the cohomologieswith coefficients in Z_2 of such Lagrangian submanifolds are isomorphic to thatof SU(3)/(SO(3) Z_3) and SU(3)/Z_3, respectively. Secondly, we calculate theFloer cohomology of a monotone Lagrangian submanifold SU(p)/Z_p in CP^{p^2-1}with coefficients in Z_2 by using Biran-Cornea's theory.

Symplectic topology of Lagrangian submanifolds of CP^n with intermediate minimal Maslov numbers