On the curvature of moduli space of special Lagrangian submanifolds

Antonella Nannicini

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 2, page 349-362
  • ISSN: 0392-4041

Abstract

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In this paper we study the curvature tensor of the Riemannian metric defined in a natural way on the moduli space of compact special Lagrangian submanifolds of a Calabi-Yau manifold. We state some curvature properties and we prove that the Ricci curvature is non negative under an assumption on the determinant of g .

How to cite

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Nannicini, Antonella. "On the curvature of moduli space of special Lagrangian submanifolds." Bollettino dell'Unione Matematica Italiana 5-B.2 (2002): 349-362. <http://eudml.org/doc/196241>.

@article{Nannicini2002,
abstract = {In this paper we study the curvature tensor of the Riemannian metric defined in a natural way on the moduli space of compact special Lagrangian submanifolds of a Calabi-Yau manifold. We state some curvature properties and we prove that the Ricci curvature is non negative under an assumption on the determinant of $g$.},
author = {Nannicini, Antonella},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {349-362},
publisher = {Unione Matematica Italiana},
title = {On the curvature of moduli space of special Lagrangian submanifolds},
url = {http://eudml.org/doc/196241},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Nannicini, Antonella
TI - On the curvature of moduli space of special Lagrangian submanifolds
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/6//
PB - Unione Matematica Italiana
VL - 5-B
IS - 2
SP - 349
EP - 362
AB - In this paper we study the curvature tensor of the Riemannian metric defined in a natural way on the moduli space of compact special Lagrangian submanifolds of a Calabi-Yau manifold. We state some curvature properties and we prove that the Ricci curvature is non negative under an assumption on the determinant of $g$.
LA - eng
UR - http://eudml.org/doc/196241
ER -

References

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  1. GROMOV, M., Pseudo holomorphic curves in symplectic manifolds, Inventiones Mathematicae, 82 (1985), 307-347. Zbl0592.53025MR809718
  2. HITCHIN, N. J., The moduli space of special Lagrangian submanifolds, Annali Scuola Normale Superiore di Pisa, (to appear) dg-ga/9711002. Zbl1015.32022MR1655530
  3. MCLEAN, R. C., Deformations of calibrated submanifolds, Duke University preprint, January (1996). Zbl0929.53027MR1664890
  4. RUUSKA, V., Riemannian polarizations, Ann. Acad. Sci. Fenn. Math. Diss. No. 106 (1996). Zbl0862.53028MR1413839
  5. SMOCZYK, K., A canonical way to deform a Lagrangian submanifold, dg-ga/9605005. 
  6. STROMINGER, A.- YAU, S.-T.- ZASLOV, E., Mirror Symmetry is T -duality, Nuclear Phys. B, 479, no. 1-2 (1996), 243-259. Zbl0896.14024MR1429831

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