Index

2D system, 127, 221

3D consistency, 128, 151, 158, 221, 224,

225, 261, 314, 316

3D system, 34, 44, 63, 67, 89, 272

4D consistency, 36, 37, 45, 63, 70, 91, 272

5-point sphere, 146

A-net, 66, 82, 119, 130

convergence, 199

in a quadric, 121

A-surface, 11, 66

associated family, 180, 211

associated point, 99, 121

asymptotic line parametrized surface, 11,

66

B¨ acklund transformation, xvi, xviii, 21,

133, 142, 179, 209, 211, 214, 224, 318

convergence, 205

Bianchi permutability, xviii, 212, 215

Bianchi quadrilateral, 1

bilinear cube equation, 277

bilinear Hirota equation, 285

bilinear octahedron equation, 285

biquadratic, 240

nondegenerate, 241

Brianchon theorem, 165, 366

Calapso transformation, 182

Carnot theorem, 364

Cauchy problem, 228

Cauchy-Riemann equation, 291, 292, 294

integrable, 297

Chebyshev net, 20

Chebyshev quadrilateral, 130, 145, 179, 282

Christoffel dual net, 7, 23, 27, 49, 58, 156,

168, 175, 176

circle pattern, 311

integrable, 317

isoradial, 317

circular net, 88, 117, 145, 177

convergence, 202, 203

Clifford algebra, 349

Clifford configuration, 147

Clifford group, 349

Clifford’s chain of theorems, 121

Combescure transformation, 5, 47, 170

commuting flows, xvi, xviii, 209

conical net, 103, 117, 177

conjugate harmonic function, 291, 292

conjugate net, 2

contact element, 17, 106, 118, 177, 336, 354

continuous limit, xviii, 42, 60, 160

cross-ratio, 24, 77, 121, 147, 173, 357

cross-ratio equation, 222, 314

in associative algebra, 236

curvature line parametrized surface, 16, 88,

115

Darboux system, 4, 42, 273

Darboux transformation, xvi, xviii, 23, 26,

151

Desargues theorem, 149, 361

discrete

wa−1,

320

discrete

za,

320

discrete Amsler surface, 180

discrete asymptotic net, 66

discrete BKP equation, 81, 277

discrete Calapso equation, 237

discrete conjugate net, 32

discrete differential geometry, xiii, xviii

401