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Abstract

Toward the end of chapter 1, we met the heat and wave equations on compact regions of the plane. We also met billiard balls travelling in those regions, bouncing off of the sides. In §§1.8.6 we asked whether there might be links between these two completely different mathematical stories: elementary physics of fields in planar regions and long term geometry of billiard ball trajectories.

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References

  1. And, if we demand a few simple properties from it, then it is unique.

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  2. Or thermodynamical, or fluid mechanical, or electrostatic. Indeed, analogies of many different physical theories can be implemented in Riemannian geometry.

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  3. In the sense of Cartan’s theory of G structures.

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  4. Again, in the sense of G structures.

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© 2003 Springer-Verlag Berlin Heidelberg

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Berger, M. (2003). Transition: The Next Two Chapters. In: A Panoramic View of Riemannian Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18245-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-18245-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65317-2

  • Online ISBN: 978-3-642-18245-7

  • eBook Packages: Springer Book Archive

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