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June 2005 Hamiltonian Minimal Lagrangian Cones in ${\mathbb C}^{m}$
Hiroshi IRIYEH
Tokyo J. Math. 28(1): 91-107 (June 2005). DOI: 10.3836/tjm/1244208282


We give a correspondence among a Hamiltonian minimal Lagrangian cone in ${\mathbb C}^{m}$, a Legendrian minimal Legendrian submanifold in the unit sphere $S^{2m-1}(1)$ and a Hamiltonian minimal Lagrangian submanifold in the complex projective space ${\mathbb C}P^{m-1}$. As an application of this result, we prove that a Hamiltonian minimal Lagrangian cone in ${\mathbb C}^{m}$ such that the first Betti number of its link is 0 must be a special Lagrangian cone. Moreover, we construct Hamiltonian minimal (non-minimal) Lagrangian cones in ${\mathbb C}^{3}$ with a toroidal link, which are parametrized by a triple of relatively prime positive integers $(p,q,r)$, and discuss their Hamiltonian stabilities.


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Hiroshi IRIYEH. "Hamiltonian Minimal Lagrangian Cones in ${\mathbb C}^{m}$." Tokyo J. Math. 28 (1) 91 - 107, June 2005.


Published: June 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1087.53057
MathSciNet: MR2149626
Digital Object Identifier: 10.3836/tjm/1244208282

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics


Vol.28 • No. 1 • June 2005
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