標(biāo)題: Titlebook: Introduction to Smooth Manifolds; John M. Lee Textbook 2012Latest edition Springer Science+Business Media New York 2012 Frobenius theorem. [打印本頁] 作者: 游牧 時間: 2025-3-21 18:41
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作者: 悲痛 時間: 2025-3-21 22:31
John M. LeeNew edition extensively revised and clarified, and topics have been substantially rearranged.Introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, mu作者: 敏捷 時間: 2025-3-22 01:13
Graduate Texts in Mathematicshttp://image.papertrans.cn/i/image/474177.jpg作者: 首創(chuàng)精神 時間: 2025-3-22 06:27
978-1-4899-9475-2Springer Science+Business Media New York 2012作者: Ptsd429 時間: 2025-3-22 12:19
Introduction to Smooth Manifolds978-1-4419-9982-5Series ISSN 0072-5285 Series E-ISSN 2197-5612 作者: 鎮(zhèn)痛劑 時間: 2025-3-22 16:40
Smooth Maps,t under diffeomorphisms. At the end of the chapter, we introduce a powerful tool for blending together locally defined smooth objects, called .. They are used throughout smooth manifold theory for building global smooth objects out of local ones.作者: Carcinogenesis 時間: 2025-3-22 18:48
Tangent Vectors, called the . of the map, and a smooth curve determines a tangent vector at each point, called its .. In the final two sections we discuss and compare several other approaches to defining tangent spaces, and give a brief overview of the terminology of ., which puts the tangent space and differentials in a larger context.作者: upstart 時間: 2025-3-23 01:01
Submersions, Immersions, and Embeddings,s this discussion is the ., a corollary of the inverse function theorem, which we prove in the first section of the chapter. Then we delve more deeply into smooth embeddings and smooth submersions, and apply the theory to a particularly useful class of smooth submersions, the ..作者: 性別 時間: 2025-3-23 03:38
,Sard’s Theorem,ontinuous map between smooth manifolds is homotopic to a smooth map. The third result is the ., which says, among other things, that embedded submanifolds can always be deformed slightly so that they intersect “nicely” in a certain sense that we will make precise.作者: Palpate 時間: 2025-3-23 07:57
Lie Groups,are also smooth submanifolds), which lead to a number of new examples of Lie groups. After explaining these basic ideas, we introduce actions of Lie groups on manifolds, which are the primary . of Lie groups. At the end of the chapter, we briefly touch on group representations.作者: Spinal-Fusion 時間: 2025-3-23 12:23 作者: Encapsulate 時間: 2025-3-23 14:36 作者: 減去 時間: 2025-3-23 21:43
Differential Forms,as the gradient, divergence, and curl operators of multivariable calculus. At the end of the chapter, we will see how the exterior derivative can be used to simplify the computation of Lie derivatives of differential forms.作者: palette 時間: 2025-3-23 23:55
Textbook 2012Latest editionneed in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras,作者: 閑蕩 時間: 2025-3-24 05:33
Integral Curves and Flows,s. We then introduce the ., which is a coordinate-independent way of computing the rate of change of one vector field along the flow of another. In the last section, we apply flows to the study of first-order partial differential equations.作者: SPASM 時間: 2025-3-24 06:31 作者: 尊重 時間: 2025-3-24 12:43 作者: 心神不寧 時間: 2025-3-24 17:05
De Rham Cohomology,n terms of those of its open subsets. Using it, we compute the de Rham groups of spheres and the top-degree groups of compact manifolds, and give a brief introduction to degree theory for maps between compact manifolds of the same dimension.作者: conformity 時間: 2025-3-24 20:52
Distributions and Foliations, chapter, the ., tells us that involutivity is also sufficient for the existence of an integral manifold through each point. At the end of the chapter, we give applications of the theory to Lie groups and to partial differential equations.作者: 過去分詞 時間: 2025-3-25 00:31
Submanifolds,folds, called ., which have the subspace topology inherited from their containing manifolds. Next, we introduce a more general kind of submanifolds, called ., which turn out to be the images of injective immersions. At the end of the chapter, we show how the theory of submanifolds can be generalized to the case of submanifolds with boundary.作者: 救護(hù)車 時間: 2025-3-25 05:44
Vector Bundles,n go on to discuss local and global sections of vector bundles (which correspond to vector fields in the case of the tangent bundle). At the end of the chapter, we discuss the natural maps between bundles, called ., and subsets of vector bundles that are themselves vector bundles, called ..作者: Tracheotomy 時間: 2025-3-25 09:14
Riemannian Metrics,fter defining Riemannian metrics and the main constructions associated with them, we show how submanifolds of Riemannian manifolds inherit induced Riemannian metrics. Then we show how a Riemannian metric leads to a distance function, which allows us to consider connected Riemannian manifolds as metric spaces.作者: 菊花 時間: 2025-3-25 12:40 作者: 平庸的人或物 時間: 2025-3-25 17:58
Vector Fields,t under left multiplication is closed under Lie brackets, and thus forms an algebraic object naturally associated with the group, called the .. We show how Lie group homomorphisms induce homomorphisms of their Lie algebras, from which it follows that isomorphic Lie groups have isomorphic Lie algebras.作者: 歡呼 時間: 2025-3-25 22:25
The de Rham Theorem,hey can be computed by restricting attention only to smooth simplices. In the final section of the chapter, we prove the de Rham theorem by showing that integration of differential forms over smooth simplices induces isomorphisms between the de Rham groups and the singular cohomology groups.作者: 強行引入 時間: 2025-3-26 00:25
0072-5285 s, the rank theorem and the fundamental theorem on flows, mu.This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures作者: 迅速成長 時間: 2025-3-26 04:35 作者: 核心 時間: 2025-3-26 10:03
John M. Leeplines, the proposed encyclopedia will have a wide audience including graduate students, researchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.作者: 娘娘腔 時間: 2025-3-26 16:16 作者: 大范圍流行 時間: 2025-3-26 20:21
John M. Leeplines, the proposed encyclopedia will have a wide audience including graduate students, researchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.作者: aspect 時間: 2025-3-26 22:27
John M. Leeplines, the proposed encyclopedia will have a wide audience including graduate students, researchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.作者: intangibility 時間: 2025-3-27 01:06
esearchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.978-94-007-7864-1作者: Licentious 時間: 2025-3-27 06:03 作者: Diskectomy 時間: 2025-3-27 12:43 作者: 難取悅 時間: 2025-3-27 14:46
John M. Leeesearchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.978-94-007-7864-1作者: transient-pain 時間: 2025-3-27 17:53
John M. Leeesearchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.978-94-007-7864-1作者: GULF 時間: 2025-3-28 01:50
John M. Leeesearchers and different levels of scientists in biomedicine, cellular and molecular biology, bioengineering, physiological and biochemistry, and pharmacology across both academia and industry.978-94-007-7864-1作者: 昆蟲 時間: 2025-3-28 02:35
0072-5285 w topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equatio978-1-4899-9475-2978-1-4419-9982-5Series ISSN 0072-5285 Series E-ISSN 2197-5612 作者: Original 時間: 2025-3-28 09:44 作者: institute 時間: 2025-3-28 12:30
ensive covering of all the terms and concepts pertaining to The Encyclopedia of Lipidomics will present a complete overview of the field from fundamentals to new discoveries and from concepts, theories and experimental techniques to clinical and industrial applications. The book will develop with th作者: violate 時間: 2025-3-28 16:26 作者: LANCE 時間: 2025-3-28 20:41
John M. Leeensive covering of all the terms and concepts pertaining to The Encyclopedia of Lipidomics will present a complete overview of the field from fundamentals to new discoveries and from concepts, theories and experimental techniques to clinical and industrial applications. The book will develop with th作者: Generosity 時間: 2025-3-28 23:24 作者: 玉米棒子 時間: 2025-3-29 06:13
John M. Leeensive covering of all the terms and concepts pertaining to The Encyclopedia of Lipidomics will present a complete overview of the field from fundamentals to new discoveries and from concepts, theories and experimental techniques to clinical and industrial applications. The book will develop with th作者: macrophage 時間: 2025-3-29 10:51
John M. Leerimental techniques to clinical and industrial applications. The book will develop with the active involvement of a strong editorial board comprised of leaders from the field. The Encyclopedia of Lipidomics intends to be a comprehensive reference resource serving to bridge the gap between clinical a作者: CLAM 時間: 2025-3-29 15:16
John M. Leerimental techniques to clinical and industrial applications. The book will develop with the active involvement of a strong editorial board comprised of leaders from the field. The Encyclopedia of Lipidomics intends to be a comprehensive reference resource serving to bridge the gap between clinical a作者: Distribution 時間: 2025-3-29 17:08 作者: acrobat 時間: 2025-3-29 19:47
John M. Leeensive covering of all the terms and concepts pertaining to The Encyclopedia of Lipidomics will present a complete overview of the field from fundamentals to new discoveries and from concepts, theories and experimental techniques to clinical and industrial applications. The book will develop with th作者: 津貼 時間: 2025-3-30 00:13 作者: 吵鬧 時間: 2025-3-30 07:06 作者: Neutropenia 時間: 2025-3-30 09:33 作者: 孤僻 時間: 2025-3-30 16:18
Smooth Maps,chapter we carry out that project. We begin by defining smooth real-valued and vector-valued functions, and then generalize this to smooth maps between manifolds. We then focus our attention for a while on the special case of ., which are bijective smooth maps with smooth inverses. If there is a dif作者: 殺子女者 時間: 2025-3-30 16:59
Tangent Vectors,of as a sort of “l(fā)inear model” for the manifold near the point. Motivated by the fact that vectors in ?. act on smooth functions by taking their directional derivatives, we define a tangent vector to a smooth manifold to be a linear map from the space of smooth functions on the manifold to ? that sa作者: 預(yù)示 時間: 2025-3-30 23:03
Submersions, Immersions, and Embeddings,erentials are surjective everywhere), . (whose differentials are injective everywhere), and . (injective smooth immersions that are also homeomorphisms onto their images). Smooth immersions and embeddings, as we will see in the next chapter, are essential ingredients in the theory of submanifolds, w作者: 騷擾 時間: 2025-3-31 01:59
Submanifolds,ituation is quite a bit more subtle than the analogous theory of topological subspaces. We begin by defining the most important type of smooth submanifolds, called ., which have the subspace topology inherited from their containing manifolds. Next, we introduce a more general kind of submanifolds, c作者: 角斗士 時間: 2025-3-31 05:45
,Sard’s Theorem,. After proving the theorem, we use it to prove three important results about smooth manifolds. The first result is the ., which says that every smooth manifold can be smoothly embedded in some Euclidean space. (This justifies our habit of visualizing manifolds as subsets of ?..) The second result i作者: 組成 時間: 2025-3-31 10:11
Lie Groups,ng many examples of interesting manifolds themselves, they are essential tools in the study of more general manifolds, primarily because of the role they play as groups of symmetries of other manifolds. We begin with the definition of Lie groups and some of the basic structures associated with them,作者: Mirage 時間: 2025-3-31 17:23
Vector Fields,tain kinds of maps from the manifold to its tangent bundle. Then we introduce the . operation, which is a way of combining two smooth vector fields to obtain another. The most important application of Lie brackets is to Lie groups: the set of all smooth vector fields on a Lie group that are invarian
