Infinitesimal affine geometry of metric spaces endowed with a dilatation structure
Infinitesimal affine geometry of metric spaces endowed with a dilatation structure
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具有膨胀结构的度量空间的无穷小仿射几何
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发表时间：
2008
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通讯作者：
Marius Buliga
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作者：
Marius Buliga
我们研究了具有膨胀结构的度量空间的代数和几何性质，这些膨胀结构是在通过越来越小的尺度时涌现的。在这个极限下，我们得到了度量仿射几何的推广，赋予了非对易向量加法运算和三个共线点之比的修正形式。这是赋范仿射群空间的几何，它是一个包含齐次群、卡诺群或可缩群的范畴。在这个范畴中，群运算不是基本的，而是派生的对象，仿射几何的推广不是基于关联关系。
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 groups. In this category group operations are not fundamental, but derived objects, and the generalization of affine geometry is not based on incidence relations.