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ON THE MASLOV INDEX OF LAGRANGIAN SUBMANIFOLDS OF GENERALIZED CALABI–YAU MANIFOLDS

PAOLO DE BARTOLOMEIS

Dipartimento di Matematica Applicata G. Sansone, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy

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and

ADRIANO TOMASSINI

Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, 43100 Parma, Italy

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https://doi.org/10.1142/S0129167X06003710Cited by:12 (Source: Crossref)

Abstract

We characterize the special Lagrangian submanifolds of a generalized Calabi–Yau manifold, with vanishing Maslov class. Then, we carefully describe several examples, including a non-Kähler generalized Calabi–Yau manifold foliated by special Lagrangian submanifolds.

Keywords:

AMSC: 53C15, 53D99, 58A14

References

C. Benson and C. S. Gordon, Topology 27, 513 (1988). Crossref, Web of Science, Google Scholar
J. L. Brylinski, J. Differential Geom. 28(1), 93 (1988). Crossref, Web of Science, Google Scholar
L. Cordero, M. Fernandez and A. Gray, Topology 25, 375 (1986). Crossref, Web of Science, Google Scholar
P. Dazord, Ann. Sci. Éc. Norm. Sup. 4 Série 13, 465 (1981). Google Scholar
P. de Bartolomeis, Ann. Mat. Pura Appl. IV CLXXIX, 361 (2001). Google Scholar
P. de Bartolomeis and G. Tian, J. Differential Geom. 43(2), 231 (1996). Crossref, Web of Science, Google Scholar
P. de Bartolomeis and A. Tomassini, Int. Math. Res. Notices 24, 1287 (2001). Google Scholar
K. Fukaya, Geometry and Physics of Branes (Como, 2001), Series in High Energy Physics, Cosmology and Gravitation (IOP, Bristol, 2003) pp. 121–209. Google Scholar
K. Fukaya, Y. G. Oh, H. Ohta and K. Ono, Lagrangian intersection, Flöer theory, anomaly and obstruction, preprint (2000),http://www.kums.kyoto-u.ac.jp/fukaya/fukaya.html . Google Scholar
N. J. Hitchin, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25(3–4), 503 (1998). Google Scholar
N. J. Hitchin, J. Differential Geom. 55, 547 (2000). Crossref, Web of Science, Google Scholar
N. J. Hitchin, Quart. J. Math. 54(3), 281 (2003). Crossref, Web of Science, Google Scholar
A. Malcev, Amer. Math. Soc. Trans. 42, 276 (1951). Web of Science, Google Scholar
S. A. Merkulov, Int. Math. Res. Notices 14, 727 (1998). Google Scholar
K. Nomizu, Ann. Math. 59, 531 (1954). Crossref, Web of Science, Google Scholar
D. Yan, Adv. Math. 120, 143 (1996). Crossref, Web of Science, Google Scholar
I. Vaisman, J. Geom. Phys. 7(3), 383 (1990). Crossref, Web of Science, Google Scholar
C. Viterbo, Bull. Soc. Math. France 115, 361 (1987). Web of Science, Google Scholar