Abstract
We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.
Citation
Toshizumi Fukui. Juan J. Nuño-Ballesteros. "Isolated roundings and flattenings of submanifolds in Euclidean spaces." Tohoku Math. J. (2) 57 (4) 469 - 503, December 2005. https://doi.org/10.2748/tmj/1140727069
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