Special Lagrangian submanifolds in the complex sphere

Henri Anciaux

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 2, page 215-227
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Anciaux, Henri. "Special Lagrangian submanifolds in the complex sphere." Annales de la faculté des sciences de Toulouse Mathématiques 16.2 (2007): 215-227. <http://eudml.org/doc/10042>.

@article{Anciaux2007,
abstract = {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.},
author = {Anciaux, Henri},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {special Lagrangian submanifolds; branes; string theory; mirror symmetry},
language = {eng},
number = {2},
pages = {215-227},
publisher = {Université Paul Sabatier, Toulouse},
title = {Special Lagrangian submanifolds in the complex sphere},
url = {http://eudml.org/doc/10042},
volume = {16},
year = {2007},
}

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
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 2
SP - 215
EP - 227
AB - 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.
LA - eng
KW - special Lagrangian submanifolds; branes; string theory; mirror symmetry
UR - http://eudml.org/doc/10042
ER -

References

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  10. 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). Zbl1016.53041MR1963560
  11. Oh (Y.-G.).— Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds, Invent. Math. 101, p. 501-519 (1990). Zbl0721.53060MR1062973
  12. Stenzel (M.).— Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80, no. 2, p. 151-163 (1993). Zbl0811.53049MR1233478
  13. Strominger (A.), Yau (S.-T.) & Zaslow (E.).— Mirror symmetry is T-duality, Nuclear Physics, B479, hep-th/9606040 (1996). Zbl0896.14024MR1429831
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