Semi-Riemannian Geometry

Index

• Acceleration of curve, 205, 283, 497
• Adjoint of linear map, 65
• Alternating map, 136
• Annihilator of linear map, 20
• Area of regular surface in , 551
• Atlas, 230, 338, 450

• consistent, 288

• maximal, 339

• smooth, 339, 450

• Ball, 193
• Basis for topological space, 185
• Basis for vector space, 7

• consistent, 158

• dual, 18

• extended, 9

• ordered, 9
• orthogonal, 62
• orthonormal, 62

• Bijective map, 613
• Bilinear function, 45

• alternating, 46

• matrix of, 47

• negative definite, 46
• nondegenerate, 46

• positive definite, 46

• symmetric, 46

• Boost, 591
• Boundary chart, 450
• Boundary of set in topological space, 184
• Boundary of smooth manifold with boundary, 451
• Boundary point, 450
• Bounded function, 192
• Bounded set in Euclidean space, 197
• Bump function, 342

• Cardinality of set, 614
• Cartan's identity, 424
• Cauchy–Binet identity, 41
• classical, 42
• Cauchy–Schwarz inequality, 51, 77

• reversed, 91

• Chain rule, 203, 204, 250, 352
• Change

• of basis, 31, 48, 100, 148
• of coordinate basis, 239, 349
• of coordinate frame, 372, 384
• of dual coordinate basis, 355
• of dual coordinate frame, 378

• Change of basis matrix, 31
• Change of variables theorem, 220
• Characteristic polynomial

• of linear map, 82
• of matrix, 81

• Characterization map, 380, 385
• Chart, 229, 337, 450

• boundary, 450

• consistent, 426
• covering, 230, 337

• interior, 450

• overlapping, ...