Einstein metrics and magnetic monopoles

Hitchin, Nigel

Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 5-29.

MR Zbl

@incollection{AST_2008__321__5_0,
     author = {Hitchin, Nigel},
     title = {Einstein metrics and magnetic monopoles},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (I) : Volume en l'honneur de Jean Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     pages = {5--29},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {321},
     year = {2008},
     mrnumber = {2521642},
     zbl = {1180.53051},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__321__5_0/}
}

TY  - CHAP
AU  - Hitchin, Nigel
TI  - Einstein metrics and magnetic monopoles
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 5
EP  - 29
IS  - 321
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2008__321__5_0/
LA  - en
ID  - AST_2008__321__5_0
ER  -

%0 Book Section
%A Hitchin, Nigel
%T Einstein metrics and magnetic monopoles
%B Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 5-29
%N 321
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2008__321__5_0/
%G en
%F AST_2008__321__5_0

Hitchin, Nigel. Einstein metrics and magnetic monopoles, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 5-29. http://www.numdam.org/item/AST_2008__321__5_0/

Bibliographie
Cité par

[1] M. Atiyah - "Magnetic monopoles in hyperbolic spaces", in Vector bundles on algebraic varieties (Bombay, 1984), Tata Inst. Fund. Res. Stud. Math., vol. 11, Tata Inst. Fund. Res., 1987, p. 1-33. | MR | Zbl

[2] M. Atiyah & N. J. Hitchin - The geometry and dynamics of magnetic monopoles, M.B. Porter Lectures, Princeton University Press, 1988. | MR | Zbl

[3] A. L. Besse - Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 10, Springer, 1987. | MR | Zbl

[4] C. P. Boyer & K. Galicki - Sasakian geometry, Oxford Mathematical Monographs, Oxford University Press, 2008. | MR | Zbl

[5] S. A. Cherkis & N. J. Hitchin - "Gravitational instantons of type $D_{k}$ ", Comm. Math. Phys. 260 (2005), p. 299-317. | DOI | MR | Zbl

[6] S. A. Cherkis & A. Kapustin - "Singular monopoles and gravitational instantons", Comm. Math. Phys. 203 (1999), p. 713-728. | DOI | MR | Zbl

[7] A. S. Dancer - "Nahm's equations and hyper-Kähler geometry", Comm. Math. Phys. 158 (1993), p. 545-568. | DOI | MR | Zbl

[8] A. S. Dancer, "A family of hyper-Kähler manifolds", Quart. J. Math. Oxford Ser. 45 (1994), p. 463-478. | DOI | MR | Zbl

[9] O. Dearricott - "Positive sectional curvature on $3$ -Sasakian manifolds", Ann. Global Anal. Geom. 25 (2004), p. 59-72. | DOI | MR | Zbl

[10] L. Faybusovich & M. Gekhtman - "Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices", Phys. Lett. A 272 (2000), p. 236-244. | DOI | MR | Zbl

[11] K. Grove, B. Wilking & W. Ziller - "Positively curved cohomogeneity one manifolds and $3$ -Sasakian geometry", J. Differential Geom. 78 (2008), p. 33-111. | DOI | MR | Zbl

[12] N. J. Hitchin - "The self-duality equations on a Riemann surface", Proc. London Math. Soc. 55 (1987), p. 59-126. | DOI | MR | Zbl

[13] N. J. Hitchin, "Poncelet polygons and the Painlevé equations", in Geometry and analysis (Bombay, 1992), Tata Inst. Fund. Res., 1995, p. 151-185. | MR | Zbl

[14] N. J. Hitchin, "A new family of Einstein metrics", in Manifolds and geometry (Pisa, 1993), Sympos. Math., XXXVI, Cambridge Univ. Press, 1996, p. 190-222. | MR | Zbl

[15] A. Kapustin & E. Witten - "Electric-magnetic duality and the geometric Langlands program", Commun. Number Theory Phys. 1 (2007), p. 1-236. | DOI | MR | Zbl

[16] A. Maciocia - "Metrics on the moduli spaces of instantons over Euclidean $4$ -space", Comm.. Math. Phys. 135 (1991), p. 467-482. | DOI | MR | Zbl

[17] M. K. Murray, P. Norbury & M. A. Singer - "Hyperbolic monopoles and holomorphic spheres", Ann. Global Anal. Geom. 23 (2003), p. 101-128. | DOI | MR | Zbl

[18] O. Nash - "A new approach to monopole moduli spaces", Nonlinearity 20 (2007), 1645-1675. | DOI | MR | Zbl

[19] O. Nash, "Singular hyperbolic monopoles", Comm. Math. Phys. 277 (2008), p. 161-187. | DOI | MR | Zbl

[20] S. M. Salamon - "Differential geometry of quaternionic manifolds", Ann. Sci. Ecole Norm. Sup. 19 (1986), p. 31-55. | DOI | EuDML | Numdam | MR | Zbl

[21] R. L. E. Schwarzenberger - "Vector bundles on the projective plane", Proc. London Math. Soc. 11 (1961), p. 623-640. | DOI | MR | Zbl

[22] K. L. Vaninsky - "The Atiyah-Hitchin bracket and the open Toda lattice", J. Geom. Phys. 46 (2003), p. 283-307. | DOI | MR | Zbl

[23] K. L. Vaninsky, "The Atiyah-Hitchin bracket and the cubic nonlinear Schrodinger equation", IMRP Int. Math. Res. Pap. (2006), p. 17683, 1-60. | MR | Zbl

[24] W. Ziller - "A new type of a positively curved manifold", preprint arXiv:0809.2304v2.