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An affine invariant characterization of flat gravity curves

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Abstract

The study of affine differential geometry is partially motivated by the fact that the direction of the affine normal coincides with the tangent direction of the gravity curve at the base point. A way to prove this is to compute the Taylor expansion of the hypersurface up to third order derivatives. By computing fourth and fifth order coefficients we characterize the second order behavior of the gravity curve at its base point in terms of affine invariants.

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  1. Institute of Mathematics, University of Lübeck, Wallstraße 40, 23560, Lübeck, Germany

    Thomas Binder

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  1. Thomas Binder
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Correspondence to Thomas Binder.

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Communicated by V. Cortés.

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Binder, T. An affine invariant characterization of flat gravity curves. Abh. Math. Semin. Univ. Hambg. 79, 265–281 (2009). https://doi.org/10.1007/s12188-009-0021-4

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  • DOI: https://doi.org/10.1007/s12188-009-0021-4

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