Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Farkas H., Kra I. — Riemann Surfaces
Farkas H., Kra I. — Riemann Surfaces

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Riemann Surfaces

Авторы: Farkas H., Kra I.

Аннотация:

This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the Abelian varities associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann -Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject. For this new edition, the material has been brought up- to-date, and erros have been corrected. The book should be of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 337

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abelian differential      49 63 226
Abel’s theorem      88
Abel’s theorem for multivalued functions      127
Accola      250
Additive multivalued function (belonging to a character)      128
Algebraic function      5
Algebraic function field      6 235
Algebraically essential singularity      227
Analytic, configuration      230
Analytic, continuation along a curve      120
Analytic, coordinate chart      11
Analytic, mapping      11
Annulus      197
Barrier at a point      161
Barrier at a point, normalized      161
Basis adapted to a point      81
Betti number      15
Bilinear relation      62
Branch      12
Branch, number (of mapping)      18
Branch, point      15 327
Branched covering      219
Canonical class      69 74
Canonical divisor      69
Canonical homology basis      6 54
Cauchy’s integral formula      34
Chain      14
Character on the fundamental group      120
Character on the fundamental group, inessential      123
Character on the fundamental group, normalized      121
Characteristic      206
Clifford index (of a divisor)      103
Clifford’s theorem      146
Closed surface      10
Cohomology class      42
Complementary divisor      104
Complex sphere      73
Complex torus      133
Conformal disc      156
Conformal mapping      11
Conjugation operator $^\ast$      23
Constant mapping      11
Coordinate chart      10
Coordinate disc      11
Covering branched      219
Covering group      191
Covering manifold      15
Covering map      15
Covering transformation      16
Curvature of metric      199 201
Cusp      203
Degree of mapping      13
Dehn twist      18
deRahm cohomology      42
Diagonalization procedure      174 178
Differentiable manifold      13
Differential form      4
Differential form, abelian      49 63 226
Differential form, abelian of the first kind      63
Differential form, abelian of the second kind      64
Differential form, abelian of the third kind      64
Differential form, associated with closed curve      39
Differential form, closed      23
Differential form, co-closed      23
Differential form, co-exact      23
Differential form, exact      23
Differential form, G-invariant form      254
Differential form, harmonic      40 43 54 226
Differential form, holomorphic      4 24 59 60
Differential form, measurable      26
Differential form, meromorphic      49
Differential form, multiplicative      122
Differential form, Prym      122
Differential form, q-canonical      69
Differential operators, $^\ast$      23 59
Differential operators, d, $\partial$, $\bar{\partial}$      22
Dimension of divisor      70
Dirichlet, principle      47 172
Dirichlet, problem      151 161
Disc (corresponding to a puncture)      214
Discontinuous group      2 188 207
Discrete group      189
Divisor      68
Divisor, canonical      69
Divisor, class group      68
Divisor, Clifford index of      103
Divisor, complementary      104
Divisor, dimension of      70
Divisor, equivalence of      68
Divisor, free points in      119
Divisor, greatest common divisor      104
Divisor, group      68
Divisor, index of specialty of      70
Divisor, integral      69
Divisor, least common multiple      105
Divisor, of multiple of      94
Divisor, polar      69
Divisor, principal      68
Divisor, ramification      254
Divisor, special      90 104
Divisor, strictly integral      94
Divisor, zero      69
Double (of a Riemann surface)      47
Earle      275
Eichler trace formula      264
Elementary group      190
Elliptic function      4
Elliptic Mobius transformation      193
Elliptic surface      94 164
Equivalent divisors      68
Essential analytic singularity      228
Euclidean metric      200
Euler( — Poincare) characteristic      6 18
Exceptional Riemann surface      192
Extended complex plane      10
Finite sheeted cover      13
Finite type      206
Free points (in a divisor)      119
Fuchsian equivalent      207
Fuchsian group      189
Fuchsian group of first kind      192
Fuchsian group of second kind      192
Function, additive      128
Function, algebraic      5
Function, element      98 120
Function, elliptic      4
Function, field      2 235
Function, group      189 207
Function, harmonic      24 151
Function, holomorphic      11
Function, meromorphic      11
Function, multiplicative      7 121 283
Function, subharinonic      156
Function, superharmonic      156
Fundamental domain      206
Fundamental group      14 194
g-hyperelliptic      319
G-invariant differential      254
Gap      78
Gauss — Bonnet formula      205
Genus of a surface      6 17 206
Geodesic      200 202
Germ (of a meromorphic function)      120 227
Greatest common divisor (of two divisors)      104
Green’s function      166
Group of divisors      68
Group, covering      16 191
Group, discontinuous      2 188 207
Group, discrete      189
Group, divisor class      68
Group, elementary      190
Group, Fuchsian      189
Group, function      189 207
Group, fundamental      14 194
Group, homology      15
Group, Kleinian      189
Group, symplectic      270
Group, unimodular      198
Guerrero      257
Half plane (corresponding to a puncture)      214
Half-period      286
Harmonic differential      40 43 54 226
Harmonic form      24
Harmonic function      24 151
Harmonic measure      165 167
Harmonization      157
Harnack’s inequality      153
Harnack’s principle      154
Hodge theorem      42
Holomorphic differential      4 59 60
Holomorphic form      24
Holomorphic function      11
Holomorphic mapping      11
Holomorphic q-differential      77
Homology group      15
Hurwitz’s theorem      242 244 325
Hyperbolic Mobius transformation      193
Hyperbolic Riemann surface      164
Hyperelliptic, involution      101
Hyperelliptic, surface      86 327
Inessential character      123
Integral divisor      69
Integration by parts      26
Intersection number (of two curves)      53
Invariant metric      201
Irreducible subvariety      145
Isometry      199
Jacobi inversion theorem      6 92 128 294
Jacobian variety      8 87 99 137
Kleinian group      189
Komiya      325
Kuribayashi      325
Least common multiple (of two divisors)      105
Lefschetz fixed point formula      265
Limit set      188
Local coordinate      11
Local parameter      11
Loxodromic Mobius transformation      193
Manifold, differentiable      13
Manifold, universal covering      2
Manifold, unlimited covering      15
Mapping, analytic      11
Mapping, conformal      11
Mapping, constant      11
Mapping, holomorphic      11
Measurable 1-form      26
Meromorphic differential      49
Meromorphic function      11
Meromorphic q-differential      49
Metric, Euclidean      200
Metric, invariant      201
Metric, non-Euclidean      202
Metric, Poincare      202
Mobius transformation, elliptic      193
Mobius transformation, hyperbolic      193
Mobius transformation, loxodromic      193
Mobius transformation, parabolic      193
Moduli      3 196 326
Monodromy theorem      16
Multiple of a divisor      69
Multiplicative (holomorphic) function      7 121
Multiplicative differential (belonging to a character)      122
Multiplicative multivalued function (belonging to a character)      121
Multiplicity (of mapping)      12
Nnon-gap      78
Noether gap theorem      79
Noether’s theorem      149
Non-Euclidean area      202
Non-Euclidean metric (= Poincare metric)      202
Normal form      16
Normalized barrier      161
Normalized character      121
nth-integer characteristic      127
Open suiface      10
Order (of a differential)      49
Orthogonal complement      30
Orthogonal decomposition      38
Parabolic Mobius transformation      192
Parabolic Riemann surface      164
Parametric disc      11
Period matrix      133 167
Perron family      159
Perron’s principle      159
Picard group      189
Poincare metric (= non- Euclidean metric)      217
Poisson kernel      152
Polar divisor      69
Principal divisor      68
Principal part      128
Projective space      130
Prolongable Riemann surface      192
Proper solution for Dirichlet problem      161
Prym differential      122 329
Puiseaux series      228 320
Puncture      206
q-canonical class      69
q-canonical divisor      69
q-canonical mapping      129
q-canonical ramification divisor      254
q-Weierstrass point      84
Ramification number (of mapping)      12
Ramification point      15
Region of discontinuity      188
Regular point for Dirichlet problem      161
Representation of Aut M      253 271
Residue (of a differential)      49
Riemann inequality      72 223
Riemann mapping theorem      182
Riemann sphere      10 198
Riemann surface      1 9
Riemann surface of finite type      206
Riemann surface, closed      10
Riemann surface, double of      47
Riemann surface, elliptic      94 164
Riemann surface, exceptional      192 277
Riemann surface, genus (of)      17
Riemann surface, hyperbolic      164
Riemann surface, open      10
Riemann surface, parabolic      164
Riemann surface, prolongable      192
Riemann theta function      7 280
Riemann theta function, singular point of      308
Riemann theta function, singular set      299
Riemann theta function, zero set of      299
Riemann — Hurwitz formula      18 75 222
Riemann — Roch theorem      7 71 74 75 224
Riemann — Roch theorem for multivalued functions      126
Riemannian metric      198
Schwarz      242
Serre      275
Sheaf of germs      180
Sheet interchange      101
Siegel upper half space      280
Signature      206
Simple Weierstrass point      86
simplex      14
Singular point of the $\theta$-function      308
Singular set of the $\theta$-function      299
Singularity, algebraically essential      227
Singularity, essential analytic      228
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте