Differentiable manifolds

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


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.


Tangent Vector Open Cover Implicit Function Theorem Tubular Neighbourhood Local Equation 


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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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