Anholonomity in Pre-and Relativistic Geodesy

  • Erik W. GrafarendEmail author
Part of the Fundamental Theories of Physics book series (FTPH, volume 196)


I was invited to speak about anholonomity or the problem to find coordinate reference systems which are differentiable. In general non-differentiable functions like (pseudo) orthonormal reference systems are differentiable forms being not classical functions. These differentiable forms are the basis of Elie Cartan’s “exterior calculus”. Geodetic examples are extensively reviewed in the context of the pre-and relativistic Geodesy.



C. Lämmerzahl and D. Pützfeld, /Bremen/ invited me to speak about anholonomity in the context of Relativistic Geodesy within the WE-Heraeus Seminar. Special thanks go to D. Pützfeld, F.W. Hehl/Cologne/ and H. Quevedo/Mexico City/ for their helpful comments. In addition, I am grateful for the support of J. Müller (Hanover) on the International Reference Ellipsoid and to S. M. Kopeikin (Columbia/Missouri) on studying Relativistic Equilibrium Figures and the relativistic theory of the Geoid. Last, but not least, I am grateful to M.A. Javaid(Stuttgart) for his expert typing.


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Authors and Affiliations

  1. 1.Department of Geodesy and GeoinformaticsFaculty of Aerospace Engineering and Geodesy, Faculty of Mathematics and PhysicsStuttgartGermany

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