• Corpus ID: 7904057

# Infinitesimal affine geometry of metric spaces endowed with a dilatation structure

@article{Buliga2008InfinitesimalAG,
title={Infinitesimal affine geometry of metric spaces endowed with a dilatation structure},
author={Marius Buliga},
journal={arXiv: Metric Geometry},
year={2008}
}
• Marius Buliga
• Published 1 April 2008
• Mathematics
• arXiv: Metric Geometry
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry, endowed with a noncommutative vector addition operation and with a modified version of ratio of three collinear points. This is the geometry of normed affine group spaces, a category which contains the ones of homogeneous groups, Carnot groups or contractible…
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