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Springer G. — Introduction to Riemann Surfaces
Springer G. — Introduction to Riemann Surfaces

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Название: Introduction to Riemann Surfaces

Автор: Springer G.

Аннотация:

This well-known book is a self-contained treatment of the classical theory of abstract Riemann surfaces. The first five chapters cover the requisite function theory and topology for Riemann surfaces. The second five chapters cover differentials and uniformization. For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the Riemann-Roch theorem and other important topics. Springer's book is an excellent text for an introductory course on Riemann surfaces. It includes exercises after each chapter and is illustrated with a beautiful set of figures.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 307

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian differential of the first kind      252
Abelian differential of the second kind      256
Abelian differential of the third kind      256
Abelian integral      296
Abelianized fundamental group      130
Abel’s theorem      277
Adherent      45
Algebraic branch point      74
Algebraic function      1
Analytic configuration      71
Analytic continuation, direct      63
Analytic continuation, direct, along a chain of disks      64
Analytic continuation, direct, along a curve      64
Analytic curve      114
Analytic manifold of regular function elements      68
Analytic structure      59
Angle function      108
Arcwise connected      53
Automorphic functions      228
Barycentric coordinates      101
Barycentric mapping      101
Barycentric subdivision      102
Base for open sets      49
Basis for regular potentials      28
Behnke, H.      209 269
Beltrami equations      20
Bergman kernel function      214
Bergman, S.      214 298
Betti number      127
Bicontinuous function      52
Bilinear relations of Riemaim for abelian differentials, of the first and second kinds      260
Bilinear relations of Riemaim for abelian differentials, of the first and third kinds      257
Bilinear relations of Riemaim for abelian differentials, of the first kind      245
Birational transformation      291
Birkhoff, G.      124 290
Boundary      45
Boundary operator      125
Boundary, simplicial n-      125
Boundary-value problem      214
Branch point of order (n - 1)      76
Canonical basis for abelian differentials of the first kind      255
Canonical basis for harmonic differentials      252
Caratheodory, C      217 231
Carrier of a curve      53
Carrier of a differential      158
Cartan, E.      163
Cauchy sequence      50
Cauchy theorem      172
Chain of disks      63
Chain, simplicial n-      124
Chain, singular 1-      139
Chevalley, C      160
Circulation      13
Class $C^n$      58
Closed differential      154
Closed domain      49
Closed set      45
Closed surface      97
Closure      45
Cluster point      46
co-closed      166
Coexact      166
Coherently oriented triangles      107
Commutator      130
Compact carrier      196
Compact space      46
Complete analytic function      115
Complete metric space      50
Complex conjugation operator      172
Complex potential function in the plane      13
Complex potential function on a surface      20
Component      49
Conformal mapping      22
Conformally equivalent Riemann surfaces      61
Congruence modulo periods      281
Conjugate flow      172
Conjugate harmonic differential      172
Conjugate surfaces      217
Conjugation operator, complex      172
Conjugation operator, star      165
Connected space      48
Continuation over a curve      78
Continuous function      50
Continuum      49
Coordinate disk      54
Countability of a Riemann surface      215
Countable manifold      56
Covering manifold      76
Covering manifold, n-sheeted      80
Covering surface      93
Covering transformation      92
Cross-point      14
Curve      52
Cycle, simplicial n-      125
Cycle, singular 1-      139
Cyclic periods      259
Degenerate barycentric mapping      101
Degree of a divisor      261
Deleted neighborhood      46
Dense set      49
DeRham theorem      176
deRham, G.      176 205
Derived set      46
Differentiable curve      114
Differentiable manifold      58
Differentiable structure      58
Differential of order 0      163
Differential of order 1      152
Differential of order 2      146
Differential, positive      147
Differential, real      147
Direct sum      186
Dirichlet integral      211
Dirichlet principle      212
Discontinuous group of transformations      228
Divisor      261
Divisor, class      263
Divisor, degree of a      261
Divisor, integral      262
Divisor, order of a      261
Divisor, principal      262
Divisors, equivalence of      263
Divisors, relatively prime      262
Domain, closed      49
Domain, open      49
Double, of a Riemann surface      217
Double, of a surface      144
Edge of a simplex      95
Elementary cycle      130
Elliptic function field      293
Elliptic integral      10 38 296
Elliptic simply connected Riemann surface      225
Equipotential lines      13
Equivalence, class      52
Equivalence, relation      52
Equivalent divisors      263
Euler characteristic      143
Exact differential      154
Existence theorems      207
Exterior derivative      158
Exterior differential calculus      163
Exterior of a set      45
Field of algebraic functions      290
Field of rational functions      292
Fluid flow on a surface      18
Fluid flow, plane      12
Ford, L.      228
Function element, regular      63
Function element, singular      70
Function field, algebraic      290
Function field, elliptic      293
Function field, hyperelliptic      293
Function field, rational      292
Fundamental domain      229
Fundamental group      85
General uniformization theorem      226
Genus      11 22 121
Green’s function      218
Green’s Theorem      159
Hall, D. W.      53
Handle      122
Harmonic      169
Harmonic component      200
Hausdorff space      43
Heins, M.      113 219
Hilbert space      178
Hodge, W. V. D.      54 176 205
Holomorphic functions      60 169
Homeomorphism      52
Homologous cycles      127
Homology group, simplicial      127
Homology group, singular      139
Homotopy of curves      81
Hurwitz, A.      274
Hyperbolic simply connected Riemann surface      225
Hyperelliptic function field      293
Hyperelliptic integral      296
Induced orientation      106
Infinitesimal transformation      242
Inner product      178
Inner product of differentials      181
Integral divisor      262
Integral of first order differentials      154
Integral of second order differentials      150
Interior point      44
Intersection      42
Inverse curve      53
Isolated point      46
Isothermal coordinates      19
Jacobi inversion problem      281
Jacobian variety      284
Jordan region      214
Klein, F.      18 207
Knopp, K      74 230
Kodaira, K.      199
Koebe, P.      207 219 226
Lagrange interpolation formula      289
Laplace operator      166
Lebesgue number      105
Lefschetz, S.      118 176
Linearly dependent differentials      249
Linearly independent differentials      249
Linked pair of edges      120
Local coordinate system      54
Local uniformizing parameter      54
Locally compact space      47
Locally separating curves      91
Logarithmic residue      14
Loop-cuts      23
MacLane, S.      124 290
Manifold      53
Mapping      50
mapping, one-to-one      50
Mean value theorem      192
Meromorphic differential      174 256
Meromorphic function      31 174
Metric space      43
Metrizable space      49
Midpoint of a simplex      102
Moduli of a Riemann surface      292
Modulus of a differential      171
Modulus of periodicity      26
Moebius band      98
Monodromy theorem      81
Munroe, R. E.      182
Neighborhood      44
Neumann, C      207
Nevanlinna, R.      217
Nondividing simple 1-cycle      144
Noneuclidean distance      233
Noneuclidean geometry      230
Noneuclidean limit rotation      231
Noneuclidean rigid motion      231
Noneuclidean rotation      231
Noneuclidean translation      231
Nonorientable manifold      107
Norm      178
Normal barycentric coordinates      103
Normal differential of the third kind      257
Normal form of a compact orientable surface      118
Normal form of a Riemann surface      229
Normal polygon      237
Normal sets      235
Normal surface of genus g      11 24 118
Normalized abelian differential      257
One-sided curve      115
One-to-one mapping      50
Open covering      46
Open domain      49
Open set      43
Open surface      97
Order of a differential at p      261
Order of a divisor      261
Order of a function at p      261
Order of a point with respect to a curve      109
Orientable manifold      107
Oriented simplex      106
Orthogonal complement      185
Orthogonal elements      185
Orthogonal projection      197
Orthogonal subspaces      185
Osgood, W. F.      207
Paired groups      176
Parabolic simply connected Riemar surface      225
Parametric curves      21
Parametric disk      54
Partition of unity      148
Path      52
Period      26 168
Perron, O.      207
Picard theorem      248
Piecewise analytic curve      115
Piecewise differentiable curve      115
Poincare, H.      207
Point of accumulation      46
Polar periods      259
Pole of order n, of a differential      174
Pole of order n, of a function      173
Pontrjagen, L. S.      124
Positive differential      147
Positive orientation      112
Principal divisor      262
Projection      67 76 200
Projective plane      98
Pruefer uncountable manifold      56
Pure differential      170
Ramification index      274
Rational function      1
Rational function field      292
Real differential      147
Region      49
Regular analytic function      60 169
Regular differential      173
Regular function      173
Regular potential      25
Regular region      158
Relative topology      46
Relatively prime divisors      262
Residue      174
Riemann inequality      266
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