Abstract
In this note we show the following result using the integral-geometric formula of R. Howard: Consider the totally geodesic RP 2m in CP n. Then it minimizes volume among the isotropic submanifolds in the same Z/2 homology class in CP n (but not among all submanifolds in this Z/2 homology class). Also the totally geodesic RP 2m−1 minimizes volume in its Hamiltonian deformation class in CP n. As a corollary we’ll give estimates for volumes of Lagrangian submanifolds in complete intersections in CP n.
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