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

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dc.creatorGoldstein, Edward
dc.date2004-06-16
dc.date2004-12-31
dc.date.accessioned2026-07-07T05:09:19Z
dc.date.available2026-07-07T05:09:19Z
dc.descriptionIn this note we show the following result using the integral-geometric formula of R. Howard: Consider the totally geodesic $\mathbb{R}P^{2m}$ in $\mathbb{C}P^n$. Then it minimizes volume among the isotropic submanifolds in the same $\mathbb{Z}/2$ homology class in $\mathbb{C}P^n$ (but not among all submanifolds in this $\mathbb{Z}/2$ homology class). Also the totally geodesic $\mathbb{R}P^{2m-1}$ minimizes volume in its Hamiltonian deformation class in $\mathbb{C}P^n$. As a corollary we'll give estimates for volumes of Lagrangian submanifolds in complete intersections in $\mathbb{C}P^n$.
dc.description5 pages, to be published in Asian Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0406334
dc.identifierhttp://arxiv.org/abs/math/0406334
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71586
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject53XX
dc.titleVolume minimization and estimates for certain isotropic submanifolds in complex projective spaces
dc.typetext

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