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Index

action, 5–13, 19, 55, 64, 69, 71–72,

85–86, 90–92, 105, 110, 114,

122–123, 127–128, 150–151, 154,

165–167, 176, 178–179, 189–190,

193, 195, 206–207, 210–212, 214,

218, 223, 226, 252, 292–293

action–angle variables, 4–13

almost complex structure, 202, 232, 249,

268–269

anti–self–dual (ASD)

conformal structure, 229–285

Einstein metric, 247, 249, 272

Kähler metric, 202–206, 210–211,

213, 215, 228–229, 235–236, 238,

248–249, 251, 263–265, 270, 272,

315, 343

null-Kähler metric, 250

Ricci–ﬂat metric, 191, 205, 211,

215–216, 241, 243, 256, 258,

272–282, 286

two–form, 138, 149, 197–198, 200,

205, 215, 225, 229, 234–236, 272

Arnold–Liouville theorem, 5, 8, 46–47,

58–59, 289, 293

ASDYM equations, 122–123, 126,

129–133, 138, 146, 148–149,

151–155, 229, 231, 251–252

Atiyah–Hitchin–Singer theorem,

268–269, 273, 283–284

Atiyah–Ward ansatz, 146–147

Bäcklund transformation

for integrable chiral model, 164

for Sine-Gordon, 24–25

BGPP metric, 211

Bianchi identity, 107, 110, 117, 120,

122, 196, 331

bi–Hamiltonian systems, 46–48, 240,

244

Birkhoff–Grothendieck theorem, 270,

306–307

Bogomolny bound, 97, 103–104, 117,

122, 168

Bogomolny equations, 96–98, 102–104,

117–118, 128, 151, 168

Bogomolny–Prasad–Sommerfeld (BPS)

limit, 116–119

bolt singularity, 194–195, 215

β-plane, 230

β-surface, 253–254, 267, 284–285

bundle

holomorphic, 129, 141–143, 146, 183,

270, 300, 303–307

line, 114, 146, 266, 270, 273, 278,

303–306

principal, 109–110, 113–114, 119,

122, 326

tangent, 68, 85, 89, 199, 202, 232,

254, 264–265, 289, 306, 318

trivial, 144, 304, 307

vector, 129, 141–143, 146, 182–183,

200, 263, 295, 300, 303–307,

323–327, 331

canonical bundle, 199, 270, 283, 306,

327, 331

Cartan character, 338–339, 342

Cartan–Kähler theorem, 335–343

Cartan structure equations, 196, 201,

230

Cartan test, 312, 321, 338–339, 341,

343

Cauchy integral formula, 51, 300–301

Cauchy–Kowalewska theorem, 310,

335–336, 338

Cech cohomology, 307–309

characteristic curves, 333–334

Chern class, 120–121, 182

Chern number, 100, 113–114, 121, 168,

218

Chern–Simons form, 120–122, 126, 223,

226

chiral model, 63, 157, 167, 176

compactiﬁcation, 100–101, 119, 157,

163, 176, 182, 185–186, 263,

298