Hamiltonian-minimal submanifolds in Kaehler manifolds with symmetries

2004/12/12 by Yuxin Dong, Dong, Yuxin
Mathematics · #53C42 (primary) #53D12 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C42 #msc:53D12

paper · pdf · doi:10.48550/arxiv.math/0412229

22 pages

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

Abstract

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CPⁿ and Cⁿ.

Related

• Hamiltonian Mechanic Systems on the Standard Cliffordian Kaehler Manifolds
• Examples of non-Kaehler Hamiltonian torus actions
• A compact symmetric symplectic non-Kaehler manifold
• Hamiltonian Mechanics on Quaternion Kaehler Manifolds
• V-minimal submanifolds