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The functional definition of geodesics

L. Klapka
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Abstract

In this paper a functional definition of geodesics is introduced which allows to generalize the notion of a geodesic from smooth to topological manifolds. It is shown that in the smooth case the new definition coincides with the classical definition of geodesics of a linear connection. If the smoothness is not required, it is shown by an example that the new definition includes geodesics of non-linear, homogeneous connections. Moreover, an example of generalized geodesics which does not arise from any connection is presented here.

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BibTeXRIS

L. Klapka. 1997-12-19. The functional definition of geodesics. https://arxiv.org/abs/dg-ga/9712007

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