## Tokyo Journal of Mathematics

### Hamiltonian Minimal Lagrangian Cones in ${\mathbb C}^{m}$

Hiroshi IRIYEH

#### Abstract

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.

#### Article information

Source
Tokyo J. Math., Volume 28, Number 1 (2005), 91-107.

Dates
First available in Project Euclid: 5 June 2009

https://projecteuclid.org/euclid.tjm/1244208282

Digital Object Identifier
doi:10.3836/tjm/1244208282

Mathematical Reviews number (MathSciNet)
MR2149626

Zentralblatt MATH identifier
1087.53057

#### Citation

IRIYEH, Hiroshi. Hamiltonian Minimal Lagrangian Cones in ${\mathbb C}^{m}$. Tokyo J. Math. 28 (2005), no. 1, 91--107. doi:10.3836/tjm/1244208282. https://projecteuclid.org/euclid.tjm/1244208282

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