Goldberg S.I. — Curvature and homology :: Электронная библиотека попечительского совета мехмата МГУ

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Goldberg S.I. — Curvature and homology

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Название: Curvature and homology

Автор: Goldberg S.I.

Аннотация:

A systematic and self-contained treatment, this revised edition examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. Four appendixes deal with holomorphic bisectional curvature, Gauss-Bonnet theorem and its applications, and Bochner’s Lemma.

Язык:

Рубрика: Математика/Алгебра/Гомология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 395

Добавлена в каталог: 19.03.2005

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Предметный указатель

Manifold, analytic      3
Manifold, completely parallelisable n-dimensional      89
Manifold, differentiable      4
Manifold, integral      48—49
Manifold, locally affine      27
Manifold, maximal integral      243
Manifold, of class $\infty$       3
Manifold, orientable (differentiable), of dimension n      4 19
Manifold, symplectic      259
Manifold, topological      3
MAP      see also Mapping
Map of class k      3
Map, closed conformal      265
Map, differentiable      17
Map, holomorphic      182
Map, induced      18 102
Map, natural      241
Map, regular      18
Mapping      see also Map
Mapping, gradient of      11
Mapping, sense-preserving      4
Maurer — Cartan, equations of      133
Maurer — Cartan, forms of      133
Metrical connection      51
Metrical connection in a complex manifold      159—161
Minimal hypersurface (of $E^{n+1}$ )      125
Module      57
Module, left $\Lambda$ -module      57
Module, right $\Lambda$ -module      57
Myers' Theorem      243
Natural base      6
Nerve (of a covering)      272
Non-singular matrix, real representation of      153
Normal topological space      301
Open covering (countable), locally finite      276
Open covering (countable), refinement of      273
Open covering (countable), simple      284
Open covering (countable), strong refinement of      277
Operator, co-differential      72—73
Operator, elliptic      242
Operator, exterior product      96
Operator, local      15
Operator, of type (a,b)      169
Orthogonal p-forms      71 170
Orthogonality relations      73—74
Orthonormal frames      32
p-boundaries      276
p-cocycles      59
p-cycles      58 61 276
p-form      14
p-form of constant length      112
p-form with coefficients in a complex line bundle      233
p-form, adjoint of      70
p-form, closed      15
p-form, co-differential of      72
p-form, covariant derivative of      193
p-form, exact      15
p-form, exterior      14
p-form, harmonic complex      176
p-form, integral of, over a domain      19
p-form, integral of, over a manifold      20
p-form, integral of, over a singular p-chain      62
p-form, integral of, over a singular p-simplex      62
p-form, l-form      see Linear (differential) form
p-form, L-invariant      108
p-form, period of      64
p-form, vectorial 1-form      42
p-th Homology group of a complex      58
p-th Homology group, singular, of a differentiable manifold      61 276
p-vector, decomposable      13
p-vector, exterior      13
Paracompact manifold      291
Parallel displacement along a curve      25
Parallel vector field      87
Partition of unity subordinated to a covering      20 301—302
Partition of unity subordinated to a covering, locally finite      20
Pfaffian form      46—47
Pfaffian system      47
Pfaffian system, completely integrable      47
Pfaffian system, first integral of      47
Poincare lemma      280
Poincare polynomials      144
Pole of a geodesic coordinate system      40
Polyhedron      60
Potential function      68
Principal fibre bundle      53—55
Principal fibre bundle, base space of      53—55
Principal fibre bundle, fibre of      54
Principal fibre bundle, structural group of      53—55
Projective transformation (of a Riemannian manifold)      121
Projective variety      146
Properly discontinuous group      184
Pure differential (form)      67—68
Pure forms      152
Quotient complex structure      184
r-distribution      48
Real analytic coordinates      147
Real finite-dimensional vector space, complex structure on      151
Real finite-dimensional vector space, complexification of      150
Real operator      152 166
Real projective plane      4
Real tensor      150
Real vector      150
Regular differential form      68
Regular topological space      302
Ricci curvature      see Curvature
Ricci curvature tensor      38 165
Ricci directions      38
Ricci identity      113

Ricci tensors      166—167 see
Riemann sphere      149
Riemann surface      184
Riemann surface of an algebraic function      66
Riemann surfaces, equivalence of      84
Riemannian geometry      30—35
Riemannian homogeneous manifold      111
Riemannian manifold      30
Riemannian manifold, $\delta$ -pinched      92
Riemannian manifold, conformally flat      116
Riemannian manifold, locally convex      125
Riemannian manifold, locally projectively flat      123
Riemannian metric      30
Riemannian metric, complete      55
scalar      see Scalar invariant
Scalar invariant      6
Scalar product      169—170; see also Vector fields Tensors
Schur, F.      37
Self-dual (linear) operator      80
Separable topological space      2
simplex      56—57
Simplex, dimension of      56
Simplex, faces of      272
Simplex, p-simplex      56—57 272
Singular homology      60—62
Singular p-chain      61
Singular p-chain, finite      61
Singular p-simplex      61
Singular p-simplex, faces of      61
Singular p-simplex, support of      61
Space form      85
Spherical space      84
Star isomorphism      68-71 see
Star operator      66 70 78—80 169—170
Star operator, inverse of      97
Stokes' theorem      21—22 62—63 284
Structural group      11 53
Structure, almost complex      156
Structure, almost hermitian      192 259
Structure, almost Kaehlerian      259
Structure, complex (analytic)      147
Structure, conjugate complex      155
Structure, differentiable of class k      2
Structure, equations of      29 160 161 165
Structure, hermitian      154
Structure, induced complex      147
Structure, induced, of class A      4
Structure, integrable almost complex      157
Structure, left invariant almost complex      190
Structure, real analytic      147
Submanifold      18
Submanifold, closed      18
Submanifold, invariant      192
Submanifold, open      18
Surface, geodesic (at a point)      35
Surface, regular closed      2
Symplectic group      144
Symplectic manifold      see Manifold
Tangent bundle      9—11 55
Tangent space (at a point)      6
Tensor algebra (over a vector space)      45
Tensor bundles      9—12
Tensor field      11
Tensor field, holomorphic of type $\begin{pmatrix}p&0\\q&0\end{pmatrix}$       211
Tensor product of modules (over non-commutative ring with unit)      58
Tensor product of vector spaces      41—42
Tensor space      7
Tensor space, pure      152
Tensorial p-form (at a point) of type (r, s)      42
Tensors      5—9
Tensors, (local) scalar product of      86
Tensors, commuting      154
Tensors, components of      7
Tensors, conjugate of      150
Tensors, contraction of      8
Tensors, contravariant      7
Tensors, covariant      7
Tensors, of type $\begin{pmatrix}q_1&r_1\\q_2&r_2\end{pmatrix}$       152
Tensors, of type (r, s)      7 8
Tensors, positive definite      8
Tensors, product of      7—8
Tensors, self adjoint      155
Tensors, skew-symmetric      7
Tensors, symmetric      7
Tensors, transvection of      39
Torsion forms      160
Torsion tensor (of an affine connection)      26 163
Torus      89—90
Totally geodesic hypersurface      125
Transition functions      11 54
Unit covering      3
Unitary frame (at a point)      158
Variety in $E^{n+1}$       see Minimal hypersurface
Vector fields      11
Vector fields, covariant derivative of      24
Vector fields, covariant differential of      24
Vector fields, induced by a 1-parameter group      99
Vector fields, scalar product of      30
Vector of bidegree (or type) (0, 1)      152
Vector of bidegree (or type) (1, 0)      152
Vectorial 1-form      42
Vectors, curl of      11—12
Vectors, homogeneous of degree p      13
Vectors, length of      30
Vectors, parallel tangent      25
Vectors, parallel tangent, along a curve      25
Weyl conformal curvature tensor      116
Weyl projective curvature tensor      122
Zero tensor      7

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