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An Introduction to Differential Manifolds pp 97–145Cite as

From Local to Global

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This chapter consists of variations on the following themes:

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Notes

  1. 1.

    None of this is true for complex manifolds: on a compact complex manifold, the holomorphic functions are constant by the maximum principle.

  2. 2.

    This enlightening point of view was communicated to me by Marc Troyanov.

  3. 3.

    This example is not a random example: the fact that there exists only a finite number of closed trajectories is a difficult result ( ≃ 1987).

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  1. Département de Mathématiques, Université Montpellier 2, Montpellier, France

    Jacques Lafontaine

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Lafontaine, J. (2015). From Local to Global. In: An Introduction to Differential Manifolds. Springer, Cham. https://doi.org/10.1007/978-3-319-20735-3_3

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