Introduction to Smooth Manifolds

@inproceedings{Lee2002IntroductionTS,
title={Introduction to Smooth Manifolds},
author={John M. Lee},
year={2002}
}
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22…
2,619 Citations
An introduction to manifolds
A Brief Introduction.- Part I. The Euclidean Space.- Smooth Functions on R(N).- Tangent Vectors In R(N) as Derivations.- Alternating K-Linear Functions.- Differential Forms on R(N).- Part II.
Introduction to differential and Riemannian geometry
• Mathematics
• 2020
This chapter introduces the basic concepts of differential geometry: Manifolds, charts, curves, their derivatives, and tangent spaces. The addition of a Riemannian metric enables length and angle
Integration on Manifolds
• Mathematics
• 2013
After giving some definitions and results on orientability of smooth manifolds, the problems treated in the present chapter are concerned with orientation of smooth manifolds; especially the
An introduction to Hamilton and Perelman's work on the conjectures of Poincaré and Thurston
• Mathematics
• 2006
Preface 3 Introduction 4 1 The Topology Setting 8 1.1 The Poincare conjecture 8 1.2 Some examples of 3-dimensional manifolds 9 1.3 The Sphere (or Prime) Decomposition 13 1.4 The Torus Decomposition
Notes on the Riemannian Geometry of Lie Groups
Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article
Introduction to manifolds
• L. Tu
• Computer Science
• 2007
The theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics, and one of the most basic topological invariants of a manifold, its de Rham cohomology is computed.
Symmetries on manifolds: generalizations of the radial lemma of Strauss
• Mathematics
Revista Matemática Complutense
• 2018
For a compact subgroup G of the group of isometries acting on a Riemannian manifold M we investigate subspaces of Besov and Triebel–Lizorkin type which are invariant with respect to the group action.
Lq,p -Cohomology of Riemannian Manifolds and Simplicial Complexes of Bounded Geometry
The Lq,p-cohomology of a Riemannian manifold (M, g) is defined to be the quotient of closed Lp-forms, modulo the exact forms which are derivatives of Lq-forms, where the measure considered comes from
The cohomology rings of seven dimensional primitive cohomogeneity one manifolds
approved: Christine M. Escher A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine
Jet Prolongations of Fibered Manifolds
This chapter introduces fibered manifolds and their jet prolongations. First, we recall properties of differentiable mappings of constant rank and introduce, with the help of rank, the notion of a