论文标题
实际分析歧管的几何分析
Geometric analysis on real analytic manifolds
论文作者
论文摘要
证明了代数和几何作业的合适拓扑结构对实际分析歧管和矢量束的连续性。这是使用最近到达的seminorms进行的，以实现真正的分析拓扑。还开发了对歧管之间真实分析映射空间的拓扑的新表征。为了表征这些拓扑结构，通过使用连接来给出各种喷气束的几何分解。然后，这些分解可用于表征差异几何形状的许多标准操作：代数操作，张量评估，张量场的各种升降，映射的组成等等等。除了主要结果外，还开发了许多技术，这些技术还可以促进对实际分析歧管的分析表现。
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new characterisation of the topology of the space of real analytic mappings between manifolds is also developed. To characterise these topologies, geometric decompositions of various jet bundles are given by use of connections. These decompositions are then used to characterise many of the standard operations from differential geometry: algebraic operations, tensor evaluation, various lifts of tensor fields, compositions of mappings, etc. Apart from the main results, numerous techniques are developed that will facilitate the performing of analysis on real analytic manifolds.
