On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 374-384.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give a description of a family of minimal conformally flat Lagrangian tori in $\mathbb CP^3$.
Keywords: symplectic manifold, Lagrangian submanifold, minimal Lagrangian torus, Fubini–Study metric, Fubini–Study symplectic form.
@article{MZM_2007_81_3_a6,
     author = {A. E. Mironov},
     title = {On a {Family} of {Conformally} {Flat} {Minimal} {Lagrangian} {Tori} in $\mathbb CP^3$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {374--384},
     publisher = {mathdoc},
     volume = {81},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a6/}
}
TY  - JOUR
AU  - A. E. Mironov
TI  - On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$
JO  - Matematičeskie zametki
PY  - 2007
SP  - 374
EP  - 384
VL  - 81
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a6/
LA  - ru
ID  - MZM_2007_81_3_a6
ER  - 
%0 Journal Article
%A A. E. Mironov
%T On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$
%J Matematičeskie zametki
%D 2007
%P 374-384
%V 81
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a6/
%G ru
%F MZM_2007_81_3_a6
A. E. Mironov. On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 374-384. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a6/

[1] I. Castro, F. Urbano, “New examples of minimal Lagrangian tori in the complex projective plane”, Manuscripta Math., 85:3–4 (1994), 265–281 | DOI | MR | Zbl

[2] D. Joyce, “Special Lagrangian 3-folds and integrable systems”, Adv. Studies in Pure Math. (to appear)

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

[4] A. E. Mironov, “Ierarkhiya uravnenii Veselova–Novikova i integriruemye deformatsii minimalnykh lagranzhevykh torov v $\mathbb CP^2$”, Sib. elektron. matem. izv., 1 (2004), 38–46 | MR | Zbl

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

[6] D. Joyce, “Special Lagrangian $m$-fold in $\mathbb C^m$ with symmetries”, Duke Math. J., 115:1 (2002), 1–51 | DOI | MR | Zbl

[7] I. Castro, L. Vrancken, “Minimal Lagrangian submanifolds in $\mathbb CP^3$ and the $\sinh$-Gordon equation”, Results Math., 40 (2001), 130–143 | MR | Zbl

[8] R. L. Bryant, “Conformal and minimal immersion into the 4-sphere”, J. Differential Geom., 17:3 (1982), 455–473 | MR | Zbl