Bryant R.L., Chern S.S., Gardner R.B. — Exterior differential systems :: Электронная библиотека попечительского совета мехмата МГУ

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Bryant R.L., Chern S.S., Gardner R.B. — Exterior differential systems

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Название: Exterior differential systems

Авторы: Bryant R.L., Chern S.S., Gardner R.B.

Аннотация:

A treatment of both the general theory and various applications of exterior differential systems, i.e. systems of equations on a manifold defined by equating to zero a number of exterior differential forms. The volume particularly studies the integral manifolds, that is, submanifolds satisfying all the equations of the system.

Язык:

Рубрика: Математика/Алгебра/Дифференциальная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 475

Добавлена в каталог: 12.03.2005

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Предметный указатель

      22
$J^r_{p,q} (N,M)$       22
-involutive      348
$\bar{\partial}$ -Neumann problem      458
$\delta$ -estimate      458
Acyclic      409
Anti-derivation      8
Asymptotic directions      201
Bianchi identity for the Ricci curvature      403
Bianchi identity, first      398
Bianchi identity, second      443
Bianchi operator      403
Blaschke conjecture      446
Bryant normal form      48
Calabi sequence      445
Canonical lifting      106
Canonical resolution of an involutive module      346
Cartan character      87 211 320
Cartan characteristic variety      224
Cartan integer       211 320
Cartan integer $\nu$       46
Cartan lemma      354
Cartan — Kaehler theory      58
Cartan — Kuranishi prolongation theorem      411 433
Cartan — Poincare lemma      351
Cauchy characteristic space      9
Cauchy characteristic vector field      36
Cauchy characteristics      33
Cauchy — Kowalewski theorem      416
Cauchy — Riemann equations      155
Cauchy — Riemann operator      440
Cauchy — Riemann operator, tangential      440
Cauchy — Riemann system      205
Cauchy — Riemann system, characteristic curves      36
Cauchy — Riemann system, sheaf      358
Cauchy — Riemann system, sheaf of the tableau      358
Cauchy — Riemann system, strips      35
Cauchy — Riemann system, variety      173
Cauchy — Riemann system, variety of linear Praffian system      181
Cauchy — Riemann system, variety of the tableau      391
Characters of the tableau      120
Charpit and Lagrange, equation of      35
Class of $\mathcal{I}$       30
Completely integrable      27
Complex characteristic variety      173
Complex of differential operators, adjoint complex of      449
Complex of differential operators, elliptic      454
Complex of differential operators, exactness of a formally exact analytic      420
Complex of differential operators, exactness of a formally exact elliptic      456
Complex of differential operators, existence of a formally, exact      426 427 428
Complex of differential operators, formally exact      419
Condition (F)      27
Conical subvariety      225
Connection on a vector bundle      434
Constant coefficient differential system      114
Contact form      26
Contact manifold      42
Contact system      26
Cotangent bundle      25
Cotangent space      25
CR-structure      437
CR-structure, almost      437
Curvature of      435
Cylindrical molding surface      169
Darboux framings      187
Darboux's theorem      42
de Rham sequence      436
Decomposable      6
Derivation of degree k      8
Derived flag      45
Derived length      45
Determined system      189
Differential ideal      16
Differential system with independence condition      18 105
distribution      27
Dolbeault sequence      440
Dual form      139
Ehrenpreis — Malgrange theorem      419
Eikonal equation      36 225
Einstein      2
Einstein metric      400
Elliptic differential system      190
Engel half-rank      45
Engel normal form      50
Equivalent symbol mappings      354
Equivalent tableaux      354
Existence theorem for analytic differential equations      397 416
Exterior algebra      6
Exterior differential form      16
Exterior differential ideal      16
Exterior differential system      15
Fibered manifold      394
Fibered submanifold      395
First derived system      45
First integral      46
First prolongation      149
Flow box coordinate theorem      28
Foliation      29
Form of degree p      7
Frobenius condition      27
Frobenius theorem      27
Gaussian curvature      192
Goursat normal form      54
Graded module associated to a tableau      335
Grassmann coordinate vector      7
Guillemin normal form      378 451
Hilbert function      341
Hilbert polynomial      366
Hilbert's Nullstellensatz      357
Homogeneous ideal      9
Horizontal form relative to a mapping      208
Hyperbolic, parabolic and elliptic      201
Ideal      9
In involution      62 108
Induced characteristic variety      226
Integrability conditions      27 139
Integral element      63 65
Integral element for $(\mathcal{I}, \Omega)$       105
Integral flag      74
Integral manifold      16 66
Integral manifold for $(\mathcal{I}, \Omega)$       17 105
Interior product      8
Involutive      62 108 409
Involutive linear Pfaffian system      140
Involutive prolongation of the isometric embedding system      198
Involutive sheaf      360
Involutive tableau      121
Involutive tableau of order p      318
Involutivity of characteristic variety      227
Involutivity of eikonal equation      227
jet      19 394
Jet bundle      18 394
Jet bundle as affine bundle      413
k-regular      71 222
K-singular      222
Kaehler-ordinary      69
Kaehler-regular      69
Killing vector field      442
Killing vector field, conformal      447

Koszul homology groups      337
Leaf      29
Legendre manifolds      177
Level      87
Levi-Civita connection      398
Lewy example      440
Lie derivative      31 441
Linear differential equation      402
Linear differential equation of finite type      441
Linear differential equation, existence of formal solutions of      424
Linear differential equation, formally integrable      419
Linear differential equation, prolongation of      423
Linear differential equation, symbol of      418
Linear differential operator      401
Linear differential operator of real principal type      461
Linear differential operator, compatibility condition for      417
Linear differential operator, determined elliptic      453
Linear differential operator, elliptic      453
Linear differential operator, non-characteristic covector for      450
Linear differential operator, non-characteristic subspace for      451
Linear differential operator, symbol of      403
Linear differential operator, symmetric hyperbolic      459
Linear differential operator, underdetermined elliptic      453
Linear differential system      103 110
Linear Weingarten surfaces      176 178
Linearly generated differential system      133
Local accessibility property      42
localization      354
Locally embeddable      189
Locally symmetric space      444
Locally symmetric space of constant curvature      445
Locally symmetric space, infinitesimal orbit of curvature of      444
Locally symmetric space, infinitesimal rigidity of      446
Monge equation      52
Monge equation of second order      56
Morphism of fibered manifolds      395
Morphism of fibered manifolds, prolongation of      395
Morphism of fibered manifolds, quasi-linear      397
Multivector      6
Natural coordinates      24
Newlander — Nirenberg theorem      456
Non-characteristic      37 173
Non-principal pair      75
Normal form of skew-symmetric matrix      14
Ordinary flag      73
Ordinary integral element      73
Ordinary zero      64
Overdetermined system      4
Partial differential equations of the first order      35
Partial differential equations of the second order      156
Partial differential equations, formal integrability of      410 415
Partial differential equations, formal solution of      397
Partial differential equations, linear      403
Partial differential equations, non-linear      431
Partial differential equations, obstruction to the integrability of      403
Partial differential equations, prolongation of      396 414
Partial differential equations, prolongation of the symbol of      410
Partial differential equations, solution of      36 395
Partial differential equations, symbol of      410 415
Pfaff equation      17
Pfaff problem      39
Pfaff symmetric normal form      39
Pfaff — Darboux local normal form      39
Pfaffian system      43 128
Pfaffian system, linear      130
Poincare lemma      410 436
Poisson bracket      228
Polar equations      67
Polar sequence      74
Polar space      67 >¦
Principal components      142
Principal pair      75
Projectivized cotangent bundle      41
Prolongation of a sub-bundle      409
Prolongation of an exterior differential system      149
Prolongation of the P.D.E. system      153
Prolongation sequence, theorem      431 433
Prolongation, $q^{th}$       150
Prolongation, of a morphism of vector bundles      402
Quasi-linear morphism of fibered manifolds      397
Quasi-linear morphism of fibered, symbol of      398
Quasi-regular      335
Quasi-regular basis      410
Quasi-regular module      335
Quillen's theorem      454
r-graph      26
r-jet      20
Rank of Pfaffian equation      38
Reduced characters      133 140
Regular      73
Regular flag      73
Regular integral element      73
Resolution of the sheaf of conformal Killing vector fields      449
Resolution of the sheaf of Killing vector fields      446 447
Retracting ideal      9
Retracting space      9
Retraction theorem      9
Ricci curvature      399
Riemalinian metric      398
Riemann curvature      398
Riemannian manifold of constant curvature      446
Riemannian manifold, conformally flat      446
S-immersion      238
Shift notation      344
Sophisticated Spencer sequence      432
Spencer cohomology groups      324 392 409
Spencer conjecture      456
Spencer — Neumann problem      459
Symbol of a P.D.E. system      135
Symbol, bundle      135
Symbol, module      335
Symbol, of the Pfaffian differential system      134
Symplectic manifold      41
System of partial differential equations      390
System of partial differential equations, existence of formal solutions of      393
System of partial differential equations, formal integrability      391
System of partial differential equations, formal solution of      391
System of partial differential equations, infinitesimal solution of      391
System of partial differential equations, symbol of      392
Tableau      115
Tableau of a linear Pfaffian system      133
Tableau of order p      315
Tableau, associated to an integral element      122
Tableau, associated to the P.D.E. system      116
Tableau, bundle      133
Tableau, characters of      119
Tableau, involutive      120
Tableau, mapping      180
Tableau, matrix      181
Tableau, prolongation of      118
Tautological prolongation sequence      255
Third fundamental theorem of Lie      113
Torsion      138 330
Torsion may be absorbed      138
Triply orthogonal systems      174
Truncation      348
Type numbers      45
Universal $k^{th}$ order differential operator      215
Wedge length      45
Weyl tensor      447

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