Volume minimization and estimates for certain isotropic submanifolds in complex projective spaces

2004/06/16 by Edward Goldstein, Goldstein, Edward
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #math.SG #msc:53XX

paper · pdf · doi:10.48550/arxiv.math/0406334

5 pages, to be published in Asian Journal of Mathematics

arxiv created 2004/12/31 · arxiv updated 2009/12/01

Abstract

In this note we show the following result using the integral-geometric formula of R. Howard: Consider the totally geodesic ℝP^2m in ℂPⁿ. Then it minimizes volume among the isotropic submanifolds in the same ℤ/2 homology class in ℂPⁿ (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 ℂPⁿ. As a corollary we'll give estimates for volumes of Lagrangian submanifolds in complete intersections in ℂPⁿ.

Citations

• The kinematic formula in Riemannian homogeneous spaces

Related

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