AI 中文总结
研究由超曲面包围区域及到其的自然光滑映射，考虑通过一维函数族对区域叶状划分，探讨组合典范投影所得函数的拓扑等性质，新挑战是讨论此类函数一阶导数及临界集，属可微映射奇点理论及相关应用。
AI 中文摘要
作者关注由超曲面所包围的区域以及到这些区域的自然光滑映射，这些映射尊重单位球面的典范投影，更一般地还涉及所谓的特殊一般映射和矩映射。我们考虑通过一维函数族及其零集（光滑地）对这些区域进行叶状划分的情况。包括作者在内的一些人还对通过组合典范投影得到的显式且良好的函数及其拓扑或组合性质感兴趣。这属于可微映射的奇点理论及其在微分拓扑和各种实几何中的应用。具体而言，作为新的挑战，我们讨论此类函数的一阶导数及其临界集。
英文摘要
The author is interested in regions surrounded by hypersurfaces and natural smooth maps onto them respecting the canonical projections of the unit spheres and so-called special generic maps and moment maps, more generally. We consider situations where these regions are foliated via 1-dimensional families of functions and their zero sets (smoothly). We including the author are also interested in explicit and nice functions obtained by composing the canonical projections and their topological or combinatorial properties. This is of singularity theory of differentiable maps and applications to differential topology and various real geometry. Explicitly, here, as a new challenge, we discuss the 1st derivative of such a function and critical sets of this.
Comments10 pages, 1 figure, the content is improved drastically e.g. several Theorems are added
