no. 2
Special Lagrangian submanifolds in the complex sphere
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 16 (2007) no. 2, pp. 215-227.

Nous construisons une famille de sous-variétés lagrangiennes dans la sphère complexe qui sont feuilletées par des sphères de dimension n-1. Nous décrivons celles qui sont de plus lagrangiennes spéciales pour la structure de Calabi-Yau induite par la métrique de Stenzel.

We construct a family of Lagrangian submanifolds in the complex sphere which are foliated by (n-1)-dimensional spheres. Among them we find those which are special Lagrangian with respect to the Calabi-Yau structure induced by the Stenzel metric.

@article{AFST_2007_6_16_2_215_0,
     author = {Anciaux, Henri},
     title = {Special {Lagrangian} submanifolds in the complex sphere},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {215--227},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 16},
     number = {2},
     year = {2007},
     doi = {10.5802/afst.1145},
     mrnumber = {2331538},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/afst.1145/}
}
TY  - JOUR
AU  - Anciaux, Henri
TI  - Special Lagrangian submanifolds in the complex sphere
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2007
SP  - 215
EP  - 227
VL  - 16
IS  - 2
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/articles/10.5802/afst.1145/
DO  - 10.5802/afst.1145
LA  - en
ID  - AFST_2007_6_16_2_215_0
ER  - 
%0 Journal Article
%A Anciaux, Henri
%T Special Lagrangian submanifolds in the complex sphere
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2007
%P 215-227
%V 16
%N 2
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/articles/10.5802/afst.1145/
%R 10.5802/afst.1145
%G en
%F AFST_2007_6_16_2_215_0
Anciaux, Henri. Special Lagrangian submanifolds in the complex sphere. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 16 (2007) no. 2, pp. 215-227. doi : 10.5802/afst.1145. http://www.numdam.org/articles/10.5802/afst.1145/

[Au] Audin (M.).— Lagrangian submanifolds, in Symplectic geometry of integrable Hamiltonian systems, M. Audin, A. Cannas da Silva, E. Lerman, Advanced courses in Mathematics CRM Barcelona, Birkhäuser (2003). | MR

[Br] Bryant (R.).— Some examples of special Lagrangian tori, Adv. Theor. Math. Phys. 3, no. 1, p. 83-90 (1999). | MR | Zbl

[CBLP] Cvetič (M.), Gibbons (G. W.), Lü (H.) & Pope (C. N.).— Ricci-flat metrics, harmonic forms and brane resolutions, Comm. Math. Phys. 232, no. 3, p. 457-500 (2003). | MR | Zbl

[CMU] Castro (I.), Montealegre (C. R.) & Urbano (F.).— Minimal Lagrangian submanifolds in the complex hyperbolic space, Illinois J. Math. 46, no. 3, p. 695-721 (2002). | MR | Zbl

[CU1] Castro (I.), Urbano (F.).— On a Minimal Lagrangian Submanifold of ℂ n Foliated by Spheres, Mich. Math. J., 46, p. 71-82 (1999). | MR | Zbl

[CU2] Castro (I.), Urbano (F.).— On a new construction of special Lagrangian immersions in complex Euclidean space, Q. J. Math. 55, no. 3, p. 253-265 (2004). | MR | Zbl

[Ha] Haskins (M.).— Special Lagrangian cones, Amer. J. Math. 126, no. 4, p. 845-871 (2004). | MR | Zbl

[HL] Harvey (R.), Lawson (H. B.).— Calibrated geometries, Acta Mathematica, 148, p. 47-157 (1982). | MR | Zbl

[Jo1] Joyce (D.).— U(1)-invariant special Lagrangian 3-folds in ℂ 3 and special Lagrangian fibrations. Turkish J. Math. 27, no. 1, p. 99-114 (2003). | MR | Zbl

[Jo2] Joyce (D.).— Riemannian holonomy groups and calibrated geometry, in Calabi-Yau manifolds and related geometries. Lectures from the Summer School held in Nordfjordeid, June 2001. Universitext. Springer-Verlag, Berlin (2003). | MR | Zbl

[Oh] Oh (Y.-G.).— Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds, Invent. Math. 101, p. 501-519 (1990). | MR | Zbl

[St] Stenzel (M.).— Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80, no. 2, p. 151-163 (1993). | MR | Zbl

[SYZ] Strominger (A.), Yau (S.-T.) & Zaslow (E.).— Mirror symmetry is T-duality, Nuclear Physics, B479, hep-th/9606040 (1996). | MR | Zbl

[Y] Yau (S.-T.).— On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equations I, Comm. Pure Appl. Math. 31, p. 339-411 (1978). | MR | Zbl

Cité par Sources :