光滑流形导论
出版社：世界图书出版公司北京公司
年代：2008
定价：75.0
书籍简介:
本书是一部学习光滑流形的入门教材。旨在让学生熟练的掌握和运用在数学和科学研究中的所需要的流形这个重要的工具。目次: 光滑流形；光滑映射；切向量；向量场；向量丛；余切丛；浸入，嵌入；子流形；李群行为；近似理论；张量；微分形式；定向；流形上的积分；De Rham 同调；de Rham定理；积分曲线与流；积分流形；李群和李代数。
书籍目录:
Preface
SmoothManifolds
TopologicalManifolds
TopologicalPrcpertiescfManifolds
SmoothStructures
ExamplesofSmoothManifolds
ManifoldswithBoundary
Problems
SmoothMaps
SmoothFunctionsandSmoothMaps
LieGroups
SmoothCoveringMaps
ProperMaps
PartitionsofUnity
Problems
3TangentVectors
TangentVectors
Pushforwards
ComputationsinCoordinates
TangentVectorstoCurves
AlternativeDefinitionsoftheTangentSpace
Problems
4VectorFields
TheTangentBundle
VectorFieldsonManifolds
LieBrackets
TheLieAlgebraofaLieGroup
Problems
5VectorBundles
VectorBundles
LocalandGlobalSectionsofVectorBundles
BundleMaps
CategoriesandFunctors
Problems
6TheCotangentBundle
Covectors
TangentCovectorsonManifolds
TheCotangentBundle
TheDifferentialofaFunction
Pullbacks
LineIntegrals
ConservativeCovectorFields
Problems
Submersions,Immersions,andEmbeddings
MapsofConstantRank
TheInverseFunctionTheoremandItsFriends
Constant-RankMapsBetweenManifolds
Submersions
Problems
Submanifolds
EmbeddedSubmanifolds
LevelSets
ImmersedSubmanifolds
RestrictingMapstoSubmanifolds
VectorFieldsandCovectorFieldsonSubmanifolds
LieSubgroups
VectorSubbundles
Problems
LieGroupActions
GroupActions
EquivariantMaps
ProperActions
QuotientsofManifoldsbyGroupActions
CoveringManifolds
HomogeneousSpaces
Applications
Problems
10EmbeddingandApproximationTheorems
SetsofMeasureZeroinManifolds
TheWhitneyEmbeddingTheorem
TheWhitneyApproximationTheorems
Problems
11Tensors
TheAlgebraofTensors
TensorsandTensorFieldsonManifolds
SymmetricTensors
RiemannianMetrics
Problems
12DifferentialForms
TheGeometryofVolumeMeasurement
TheAlgebraofAlternatingTensors
TheWedgeProduct
DifferentialFormsonManifolds
ExteriorDerivatives
SymplecticForms
Problems
13Orientations
OrientationsofVectorSpaces
OrientationsofManifolds
TheOrientationCovering
OrientationsofHypersurfaces
BoundaryOrientations
TheRiemannianVolumeForm
HypersurfacesinRiemannianManifolds
Problems
14IntegrationonManifolds
IntegrationofDifferentialFormsonEuclideanSpace
IntegrationonManifolds
StokessTheorem
ManifoldswithCorners
IntegrationonRiemannianManifolds
IntegrationonLieGroups
Densities
Problems
15DeRhamCohomology
ThedeRhamCohomologyGroups
HomotopyInvariance
TheMayer-VietorisTheorem
Computations
Problems
16ThedeRhamTheorem
SingularHomology
SingularCohomology
SmoothSingularHomology
ThedeRhamTheorem
Problems
17IntegralCurvesandFlows
IntegralCurves
GlobalFlows
TheFundamentalTheoremonFlows
CompleteVectorFields
RegularPointsandSingularPoints
Time-DependentVectorFields
ProofoftheODETheorem
Problems
18LieDerivatives
TheLieDerivative
CommutingVectorFields
LieDerivativesofTensorFields
ApplicationstoGeometry
ApplicationstoSymplecticManifolds
Problems
19IntegralManifoldsandFoliations
TangentDistributions
InvolutivityandDifferentialForms
TheFrobeniusTheorem
ApplicationstoPartialDifferentialEquations
Foliations
Problems
20LieGroupsandTheirLieAlgebras
One-ParameterSubgroups
TheExponentialMap
TheClosedSubgroupTheorem
TheAdjointRepresentation
LieSubalgebrasandLieSubgroups
NormalSubgroups
TheFundamentalCorrespondence
Problems
Appendix:ReviewofPrerequisites
Topology
LinearAlgebra
Calculus
References
Index
内容摘要:
本书是一部介绍光滑流形的入门教材(全英文版)。该书是针对已经对一般拓扑、基本群、覆盖空间以及基本的线性代数与实分析有较好掌握的本科生和研究生。旨在让学生和相关的工作人员熟练地掌握和运用流形这个重要的数学工具。本书主要介绍了光滑结构，切向量和余向量，向量丛，李导数，浸入和嵌入式子流形，李群和李代数。在讲述上运用图形以及直观的讨论使得内容尽可能的清晰易懂，更重要的是讲述如何用几何的方法思考抽象概念；同时，现代数学方法提供的有力工具得到了充分展示。本书还提供了一些很重要的流形能够提供的几何结构的例子。
书籍规格:
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| 书名 | 光滑流形导论站内查询相似图书 | ||
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 75.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
书籍信息归属:
光滑流形导论是世界图书出版公司北京公司于2008.03出版的中图分类号为 O189.3 的主题关于 光滑化（数学）－流形－英文 的书籍。
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