论文标题
无差异网的本地不变
Local invariants of divergence-free webs
论文作者
论文摘要
我们研究的对象是量化量差异的几何形状中的网。我们介绍了两个无分流网的本地不变性网络：一个差异性，直接与S. Tabachnikov（1992）引入的无差2-WEB自然连接的曲率和一个几何形状相关，而一个几何形状是由W. Blaschke和G. Thomsen（W. blaschke and G. thoms）定义的Planar 3-web Planar 3-web Planar 3-web Planar 3-web plassim of的启发（192）我们表明，这两个不变的两个的琐碎性都表征了无差异的网络收益，直到等效性。我们还建立了一些有关完整分类问题的初步结果，这些结果共同概括了tabachnikov链球菌的定理，这是无差异的2-webs的正常形式。它们用于在平面案例中提供规范的形式和一组通用无差网络的不变性。最后，讨论了当地琐事条件及其在数值相对性中的潜在应用的相关性。
The objects of our study are webs in the geometry of volume-preserving diffeomorphisms. We introduce two local invariants of divergence-free webs: a differential one, directly related to the curvature of the natural connection of a divergence-free 2-web introduced by S. Tabachnikov (1992), and a geometric one, inspired by the classical notion of planar 3-web holonomy defined by W. Blaschke and G. Thomsen (1928). We show that triviality of either of these invariants characterizes trivial divergence-free web-germs up to equivalence. We also establish some preliminary results regarding the full classification problem, which jointly generalize the theorem of S. Tabachnikov on normal forms of divergence-free 2-webs. They are used to provide a canonical form and a complete set of invariants of a generic divergence-free web in the planar case. Lastly, the relevance of local triviality conditions and their potential applications in numerical relativity are discussed.
