Geodesic
On Hamiltonian Minimality of Isotropic Nonhomogeneous Tori in $\mathbb{H}^n$ and $\mathbb C\mathrm P^{2n+1}$
Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 119-129 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a family of flat isotropic nonhomogeneous tori in $\mathbb{H}^n$ and $\mathbb{C}\mathrm{P}^{2n+1}$ and find necessary and sufficient conditions for their Hamiltonian minimality.
Keywords: isotropic submanifold, Hamiltonian-minimal submanifold. 
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     title = {On {Hamiltonian} {Minimality} of {Isotropic} {Nonhomogeneous} {Tori} in $\mathbb{H}^n$ and $\mathbb C\mathrm P^{2n+1}$},
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M. A. Ovcharenko. On Hamiltonian Minimality of Isotropic Nonhomogeneous Tori in $\mathbb{H}^n$ and $\mathbb C\mathrm P^{2n+1}$. Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 119-129. http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a8/

[1] Y.-G. Oh, “Volume minimization of Lagrangian submanifolds under Hamiltonian deformations”, Math Z., 212:2 (1993), 175–192 | DOI | MR | Zbl

[2] I. Castro, F. Urbano, “Examples of unstable Hamiltonian-minimal Lagrangian tori in $\mathbb C^2$”, Compositio Math., 111:1 (1998), 1–14 | DOI | MR | Zbl

[3] F. Hélein, P. Romon, “Hamiltonian stationary Lagrangian surfaces in $\mathbb C^2$”, Comm. Anal. Geom., 10:1 (2002), 79–126 | DOI | MR | Zbl

[4] F. Hélein, P. Romon, “Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions”, Comment. Math. Helv., 75:4 (2000), 668–680 | DOI | MR | Zbl

[5] A. E. Mironov, “O gamiltonovo-minimalnykh lagranzhevykh torakh v $\mathbb{C}P^2$”, Sib. matem. zhurn., 44:6 (2003), 1324–1328 | MR | Zbl

[6] H. Ma, “Hamiltonian Stationary Lagrangian Surfaces in $\mathbb C\mathrm P^2$”, Ann. Global Anal. Geom., 27:1 (2005), 1–16 | DOI | MR

[7] A. E. Mironov, “O novykh primerakh gamiltonovo-minimalnykh i minimalnykh lagranzhevykh podmnogoobrazii v $\mathbb C^n$ i $\mathbb C\mathrm P^n$”, Matem. sb., 195:1 (2004), 89–102 | DOI | MR | Zbl

[8] A. E. Mironov, T. E. Panov, “Peresecheniya kvadrik, moment-ugol-mnogoobraziya i gamiltonovo-minimalnye lagranzhevy vlozheniya”, Funkts. analiz i ego pril., 47:1 (2013), 47–61 | DOI | MR | Zbl

[9] R. A. Sharipov, “Minimalnye tory v pyatimernoi sfere v $\mathbb C^3$”, TMF, 87:1 (1991), 48–56 | MR | Zbl

[10] M. S. Ermentai, “O minimalnykh izotropnykh torakh v $\mathbb CP^3$”, Sib. matem. zhurn., 59:3 (2018), 529–534 | DOI

[11] M. A. Ovcharenko, “O gamiltonovo-minimalnykh izotropnykh odnorodnykh torakh v $\mathbb C^n$ i $\mathbb C\mathrm P^n$”, Sib. matem. zhurn., 59:5 (2018), 1171–1178 | DOI | Zbl

[12] M. S. Ermentai, “Ob odnom semeistve minimalnykh izotropnykh torov i butylok Kleina v $\mathbb{C}P^3$”, Sib. elektron. matem. izv., 16 (2019), 955–958 | DOI | Zbl

[13] B. Chen, J.-M. Morvan, “Deformations of isotropic submanifolds in Kähler manifolds”, J. Geom. Phys., 13:1 (1994), 79–104 | DOI | MR | Zbl

[14] H. B. Lawson, Lectures on Minimal Submanifolds, Publish or Perish, Wilmington, DE, 1980 | MR | Zbl

[15] A. Besse, Mnogoobraziya Einshteina, T. I, II, Mir, M., 1990 | MR