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Differentiable manifolds

  • Frédéric Pham
Part of the Universitext book series (UTX)

Abstract

Definition of a topological manifold, structures on a manifold, morphisms of manifolds, examples of differentiable manifolds. Submanifolds, embeddings, immersions. The tangent space of a differentiable manifold, the tangent map. Differential forms on a manifold, transformations of differential forms, complex-valued differential forms. Partitions of unity on a manifold, construction of a Riemannian metric, construction of a tubular neighbourhood of a closed submanifold. Orientation of manifolds. Every complex analytic manifold has a canonical orientation. The integral of a differential form on an oriented manifold. Integration on a manifold with boundary and Stokes’ formula. Appendix on complex analytic sets.

Keywords

Tangent Vector Open Cover Implicit Function Theorem Tubular Neighbourhood Local Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Frédéric Pham
    • 1
  1. 1.Laboratoire J.-A. DieudonnéUniversité de Nice Sophia AntipolisNice cedex 02France

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