## Journal of the Mathematical Society of Japan

### A special Lagrangian fibration in the Taub-NUT space

Takahiro NODA

#### Abstract

In this paper we construct explicitly a special Lagrangian fibration in the Taub-NUT space. The Taub-NUT space is a complex 2-fold with a Ricci-flat metric and it is well known to physicists. For this space, we find $S^{1}$-invariant special Lagrangian submanifolds by using moment map techniques and show that a family of special Lagrangian submanifolds give a fibration of the Taub-NUT space. We also study a topology of special Lagrangian fibers using explicit description of special Lagrangians.

#### Article information

Source
J. Math. Soc. Japan Volume 60, Number 3 (2008), 653-663.

Dates
First available in Project Euclid: 4 August 2008

http://projecteuclid.org/euclid.jmsj/1217884487

Digital Object Identifier
doi:10.2969/jmsj/06030653

Mathematical Reviews number (MathSciNet)
MR2440408

Zentralblatt MATH identifier
1146.53032

#### Citation

NODA, Takahiro. A special Lagrangian fibration in the Taub-NUT space. J. Math. Soc. Japan 60 (2008), no. 3, 653--663. doi:10.2969/jmsj/06030653. http://projecteuclid.org/euclid.jmsj/1217884487.

#### References

• A. Besse, Einstein manifolds, Springer-Verlag, New York 1987.
• G. Gibbons and S. W. Hawking, Gravitational multi-instantons, Phys. Lett., 78B (1978), 430–432.
• M. Gross and P. M. H. Wilson, Large complex structure limits of K3 surfaces, J. Differential geom., 55 (2000), 475–546.
• R. Harvey and H. Lawson, Calibrated geometries, Acta Math., 148 (1982), 47–157.
• S. W. Hawking, Gravitational Instantons, Phys. Lett., 60A (1977), 81–83.
• M. Ionel and M. Min-Oo, Cohomogeneity one special Lagrangians in the deformed conifold..
• M. Ionel and M. Min-Oo, Special Lagrangians of cohomogeneity one in the resolved conifold..
• D. D. Joyce, Compact Manifolds with Special Holonomy, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000.
• S. Karigiannis and M. Min-Oo, Calibrated subbundles in non-compact manifolds of special holonomy, Ann. Global Anal. Geom., 28 (2005), 371–394.
• C. LeBrun, Complete Ricci-Flat Kähler Metrics on $\bm{C}^n$ Need Not Be Flat, Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989), Proc. Sympos. Pure. Math., 52, Part 2, Amer. Math. Soc., Providence, RI, 1991, pp.,297–304.